new construction of 3nj symbols polynomials reducing the wavefunction of coupled momenta to products of single ones are introduced and discussed composition of n such polynomials serves as a generating function for 3nj coefficients of vector addition for su 1 1 the polynomials are calculated explicitly and a compact integral representation for 9j coefficients is obtained as an example the method is rather general and may be applied to other groups and to higher vector addition coefficients

comparison and stability of solutions to a class of quasilinear parabolic problems on presente des resultats de comparaison et d unicite pour les solutions de problemes aux valeurs limites quasilineaires paraboliques avec et sans obstacles un resultat de stabilite dans l 1 donne la stabilisation asymptotique dans cet espace quand t vers le probleme elliptique correspondant

a priori bounds and multiplicity for fully nonlinear equations with quadratic growth in the gradient abstract we consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient such as f x u d u d 2 u c x u m x d u d u h x in a bounded domain with a dirichlet boundary condition here r c h l p p n 1 c 0 and the matrix m satisfies 0 1 i m 2 i recently this problem was studied in the coercive case c 0 where uniqueness of solutions can be expected and it was conjectured that the solution set is more complex for noncoercive equations this conjecture was verified in 2015 by arcoya de coster jeanjean and tanaka for equations in divergence form by exploiting the integral formulation of the problem here we show that similar phenomena occur for general even fully nonlinear equations in nondivergence form we use different techniques based on the maximum principle we develop a new method to obtain the crucial uniform a priori bounds which permit to us to use degree theory this method is based on basic regularity estimates such as half harnack inequalities and on a vazquez type strong maximum principle for our kind of equations

comparison results for nonlinear degenerate dirichlet and neumann problems with general growth in the gradient abstract this paper deals with both dirichlet and neumann problems for a class of nonlinear degenerate elliptic equations with general growth in the gradient first we give an existence result of a spherically symmetric solution to the symmetrized problems with data depending only on the radials second we prove that the solutions of the original problems can be compared under a rearrangement with the solutions of the symmetrized problems

quasilinear elliptic equations with quadratic growth in unbounded domains on donne des resultats d existence et de regularite pour des equations elliptiques quasilineaires a croissance quadratique par rapport au gradient du type au f x u grad u 0 dans u 0 sur

quasilinear elliptic problems with singular and homogeneous lower order terms abstract we deal with singular quasilinear elliptic equations namely u u x u q u q 1 f x in u 0 in u 0 on where is a bounded smooth domain of r n n 3 r 1 q 2 0 l and 0 f l p for some p n 2 we completely describe the set of values of the parameter for which the problem admits solution thus we study existence nonexistence and uniqueness of bounded weak solutions in both cases f 0 and f 0

existence of renormalized solutions to nonlinear elliptic equations with two lower order terms and measure data in this paper we prove the existence of a renormalized solution to a class of nonlinear elliptic problems whose prototype is formula maths where is a bounded open subset of r n n 2 ap is the so called p laplace operator 1 p n is a radon measure with bounded variation on 0 p 1 0 p 1 and c and b belong to the lorentz spaces l p 1 r n p 1 r and l n 1 respectively in particular we prove the existence under the assumptions that p 1 c belongs to the lorentz space ln p 1 r n p 1 r and c n r is small enough

uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions in this paper we show that the maximum principle holds for quasilinear elliptic equations with quadratic growth under general structure conditions

realizations of su 1 1 and uq su 1 1 and generating functions for orthogonal polynomials positive discrete series representations of the lie algebra su 1 1 and the quantum algebra uq su 1 1 are considered the diagonalization of a self adjoint operator the hamiltonian in these representations and in tensor products of such representations is determined and the generalized eigenvectors are constructed in terms of orthogonal polynomials using simple realizations of su 1 1 uq su 1 1 and their representations these generalized eigenvectors are shown to coincide with generating functions for orthogonal polynomials the relations valid in the tensor product representations then give rise to new generating functions for orthogonal polynomials or to poisson kernels in particular a group theoretical derivation of the poisson kernel for meixner pollaczek and al salam chihara polynomials is obtained

convolution identities for dunkl orthogonal polynomials from the osp 1 2 lie superalgebra new convolution identities for orthogonal polynomials belonging to the q 1 analog of the askey scheme are obtained specialization of the chihara polynomials will play a central role as the eigenfunctions of a special element of the lie superalgebra osp 1 2 in the positive discrete series representation using the clebsch gordan coefficients a convolution identity for the specialized chihara the dual 1 hahn and the big 1 jacobi polynomials are found using the racah coefficients a convolution identity for the big 1 jacobi and the bannai ito polynomials is found finally these results are applied to construct a bilinear generating function for the big 1 jacobi polynomials new convolution identities for orthogonal polynomials belonging to the q 1 analog of the askey scheme are obtained specialization of the chihara polynomials will play a central role as the eigenfunctions of a special element of the lie superalgebra osp 1 2 in the positive discrete series representation using the clebsch gordan coefficients a convolution identity for the specialized chihara the dual 1 hahn and the big 1 jacobi polynomials are found using the racah coefficients a convolution identity for the big 1 jacobi and the bannai ito polynomials is found finally these results are applied to construct a bilinear generating function for the big 1 jacobi polynomials

multiplicity results in the non coercive case for an elliptic problem with critical growth in the gradient abstract we consider the boundary value problem p u c x u x u 2 h x u h 0 1 l where r n n 3 is a bounded domain with smooth boundary it is assumed that c h belong to l p for some p n with c 0 as well as l and 1 0 for some 1 r it is known that when 0 problem p has at most one solution in this paper we study under various assumptions the structure of the set of solutions of p assuming that 0 our study unveils the rich structure of this problem we show in particular that what happen for 0 influences the set of solutions in all the half space 0 h 0 1 l most of our results are valid without assuming that h has a sign if we require h to have a sign we observe that the set of solutions differs completely for h 0 and h 0 we also show when h has a sign that solutions not having this sign may exists some uniqueness results of signed solutions are also derived the paper ends with a list of open problems

results for degenerate nonlinear elliptic equations involving a hardy potential abstract consider the problem p div a x u u u s x p f x in u x 0 in u x 0 on where is an open bounded subset of r n n 3 1 p n and s are positive numbers f is a nonnegative function in some lebesgue space a r r n r n is such that c 0 a x t p 1 p a x t for some 0 1 which provides a noncoercive operator when u the problem could be seen as a reaction model which produces a saturation effect that is the diffusion goes to zero when u goes to infinity this type of reaction appears as a linearization of the arrhenius reaction in some solid combustion problems see for instance peral and vazquez 1995 21 the aim of the article is to study existence nonexistence and regularity of the solutions to problem p the main features in the paper are the following the threshold on s to have existence or nonexistence of solution in some weak sense is s p 1 1 moreover a bound on is needed to have solution in the critical case s p 1 1 the regularity of the solution according to the summability of f

the transformation theorem for two parameter pure jump martingales letm be a martingale of pure jump type i e the compensation of the process describing the total of the point jumps ofm in the plane m can be uniformly approximated by martingales of bounded variation jumping only on finitely many axial parallel lines using this fact we prove a change of variables formula in which forc4 functions f the processf m is described by integrals off k m k 1 2 with respect to stochastic integrators of the types expected a martingale two processes behaving as martingales in one direction and as processes of bounded variation in the other and one process of bounded variation hereby we are led to investigate two types of random measures not considered so far in this context by combination with the integrators already known they might complete the set needed for a general transformation formula

on the comparison principle for unbounded solutions of elliptic equations with first order terms abstract we prove a comparison principle for unbounded weak sub super solutions of the equation u div a x d u h x d u in where a x is a bounded coercive matrix with measurable ingredients 0 and h x has a super linear growth and is convex at infinity we improve earlier results where the convexity of h x was required to hold globally

on some nonlinear elliptic equations involving derivatives of the nonlinearity the existence of weak solutions of the dirichlet problem for nonlinear elliptic equations of the type x j a ij x u x i b j u a x u f is proved for nonlinearities b j which are only continuous the proof is based on the observation that an l a priori estimate is valid which is independent of b j the second part contains several uniqueness results and counterexamples showing that uniqueness may fail in general

on the existence of weak solutions to a class of nonlinear elliptic systems with drift term abstract we study the existence of a weak solution u of the following nonlinear vectorial dirichlet problem u w 0 1 2 r n i 1 n d i a i x u d u i 1 n d i j 1 n e i j x u j f x x where is a bounded subset of r n n 3 u and f for any 1 2 n are the th components of the vectors u and f respectively and the tensors a x s and e x satisfy suitable structural assumptions

comparison results and improved quantified inequalities for semilinear elliptic equations in this paper we prove some pointwise comparison results between the solutions of some second order semilinear elliptic equations in a domain omega of mathbb r n and the solutions of some radially symmetric equations in the equimeasurable ball omega the coefficients of the symmetrized equations in omega satisfy similar constraints as the original ones in omega we consider both the case of equations with linear growth in the gradient and the case of equations with at most quadratic growth in the gradient moreover we show some improved quantified comparisons when the original domain is not a ball the method is based on a symmetrization of the second order terms

quasi linear degenerate elliptic problems with l1 data abstract we prove existence and uniqueness of a solution for a class of quasi linear problems with l 1 data the diffusion matrix a x u is allowed to degenerate with respect to the unknown u we obtain uniqueness of the solution under a weak assumption on a x u that permits to consider highly oscillating or and increasing coefficients with respect to u

non linear elliptic and parabolic equations involving measure data in this paper we prove the existence of solutions for equations of the type div a du f in a bounded open set u 0 on where a is a possibly non linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure we also consider the equation div a du g u f in u 0 on with f l1 or f m u u 0 and the parabolic equivalent of the first elliptic equation

existence and comparison results for quasilinear elliptic equations with critical growth in the gradient abstract we give a condition of existence of bounded solutions for a general quasilinear elliptic problem with quadratic growth in the gradient when the data are small enough moreover we obtain an a e comparison with the semilinear symmetrized problem

existence uniqueness and homogenization of the second order slip reynolds equation the decreasing of the distance between the head and the magnetic disk surface leads to a model of the behaviour of the air by using a modified reynolds equation the existence and the uniqueness of this stationary equation is under some conditions on the data proved using both fixed point and monotonicity techniques double scale analysis allows us to obtain the associated homogenized equation

continuum of solutions for an elliptic problem with critical growth in the gradient abstract we consider the boundary value problem p u h 0 1 l u c x u x u 2 h x where r n n 3 is a bounded domain with smooth boundary it is assumed that c 0 c h belong to l p for some p n 2 and that l we explicitly describe a condition which guarantees the existence of a unique solution of p when 0 and we show that these solutions belong to a continuum the behaviour of the continuum depends in an essential way on the existence of a solution of p 0 it crosses the axis 0 if p 0 has a solution otherwise it bifurcates from infinity at the left of the axis 0 assuming that p 0 has a solution and strengthening our assumptions to x 1 0 and h 0 we show that the continuum bifurcates from infinity on the right of the axis 0 and this implies in particular the existence of two solutions for any 0 sufficiently small

hardy spaces for non compactly causal symmetric spaces and the most continuous spectrum let g h be a semisimple symmetric space then the space l2 g h can be decomposed into a finite sum of series of representations induced from parabolic subgroups of g the most continuous part of the spectrum of l2 g h is the part induced from the smallest possible parabolic subgroup in this paper we introduce hardy spaces canonically related to this part of the spectrum for a class of non compactly causal symmetric spaces the hardy space is a reproducing hilbert space of holomorphic functions on a bounded symmetric domain of tube type containing g h as a boundary component a boundary value map is constructed and we show that it induces a g isomorphism onto a multiplicity free subspace of full spectrum in the most continuous part lmc2 g h of l2 g h we also relate our hardy space to the classical hardy space on the bounded symmetric domain

nonlinear elliptic equations with natural growth in the gradient and source terms in lorentz spaces abstract in this paper we consider the problem u w 0 1 p div a x u d u b x u d u h x u d u in d where div a x u d u is a leray lions operator which is defined on w 0 1 p with coercivity where the growth with respect to du of h x u d u is controlled by d u p and where b x u d u satisfies a similar growth condition but has the good sign the main feature of the problem is that the source terms belong to the lorentz space l n p when two smallness conditions are satisfied the second one depends on the behavior of b x u d u when u tends to infinity we prove the existence of a solution which further satisfies e p 1 u 1 w 0 1 p for every with 0 for some threshold 0 the key ingredient in the proof of the existence result is an a priori estimate which holds true for every solution to the problem which satisfies the above mentioned exponential regularity condition

meixner functions and polynomials related to lie algebra representations the decomposition of the tensor product of a positive and a negative discrete series representation of the lie algebra 1 1 is a direct integral over the principal unitary series representations in the decomposition discrete terms can occur and these are a finite number of discrete series representations or one complementary series representation the interpretation of meixner functions and polynomials as overlap coefficients in the four classes of representations and the clebsch gordan decomposition lead to a general bilinear generating function for the meixner polynomials finally realizing the positive and negative discrete series representations as operators on the spaces of holomorphic and anti holomorphic functions respectively a non symmetric type poisson kernel is found for the meixner functions

reiterated ergodic algebras and applications we redefine the homogenization algebras without requiring the separability assumption we show that this enables one to treat more complicated homogenization problems than those solved by the previous theory in particular we exhibit an example of algebra which contrary to the algebra of almost periodic functions induces no homogenization algebra we prove some general compactness results which are then applied to the resolution of some homogenization problems related to the generalized reynolds type equations and to some nonlinear hyperbolic equations

nonlinear elliptic systems in stochastic game theory on etudie des systemes d equations aux derivees partielles non lineaires provenant de la theorie des jeux differentiels stochastiques au sens de nash

meixner polynomials of the second kind and quantum algebras representing su 1 1 we show how viennot s combinatorial theory of orthogonal polynomials may be used to generalize some recent results of sukumar and hodges hodges sukumar 2007 proc r soc a 463 2401 2414 doi 10 1098 rspa 2007 0001 1 sukumar hodges 2007 proc r soc a 463 2415 2427 doi 10 1098 rspa 2007 0003 2 on the matrix entries in powers of certain operators in a representation of su 1 1 our results link these calculations to finding the moments and inverse polynomial coefficients of certain laguerre polynomials and meixner polynomials of the second kind as an immediate consequence of results by koelink groenevelt and van der jeugt van der jeugt 1997 j math phys 38 2728 2740 doi 10 1063 1 531984 3 koelink van der jeugt 1998 siam j math anal 29 794 822 doi 10 1137 s003614109630673x 4 groenevelt koelink 2002 j phys a 35 65 85 doi 10 1088 0305 4470 35 1 306 5 for the related operators substitutions into essentially the same laguerre polynomials and meixner polynomials of the second kind may be used to express their eigenvectors our combinatorial approach explains and generalizes this coincidence 1 http dx doi org doi 10 1098 rspa 2007 0001 2 http dx doi org doi 10 1098 rspa 2007 0003 3 http dx doi org doi 10 1063 1 531984 4 http dx doi org doi 10 1137 s003614109630673x 5 http dx doi org doi 10 1088 0305 4470 35 1 306

quantum hypercomputation based on the dynamical algebra an adaptation of kieu s hypercomputational quantum algorithm khqa is presented the method that was used was to replace the weyl heisenberg algebra by other dynamical algebra of low dimension that admits infinite dimensional irreducible representations with naturally defined generalized coherent states we have selected the lie algebra because this algebra possesses the necessary characteristics to realize the hypercomputation and also because such algebra has been identified as the dynamical algebra associated with many relatively simple quantum systems in addition to an algebraic adaptation of khqa over the algebra we presented an adaptation of khqa over some concrete physical referents the infinite square well the infinite cylindrical well the perturbed infinite cylindrical well the poschl teller potentials the holstein primakoff system and the laguerre oscillator we conclude that it is possible to have many physical systems within condensed matter and quantum optics in which it is possible to consider an implementation of khqa

uniqueness and nonuniqueness for the approximation of quasilinear elliptic equations we investigate the issue of uniqueness and nonuniqueness for the approximate solution of quasilinear elliptic equations in particular we show that even if the continuous problem admits a unique solution its approximation by finite elements may lead to several approximate solutions

on the reynolds lubrication equation let be a bounded open set in r 2 with smooth boundary is the region where two solid bodies are in contact these two solids are moving and the average of their velocities is denoted by v v 1 v 2 the pressure p p x which develops in a fluid layer confined between these two bodies satisfies the so called reynolds lubrication equation 1 h 3 p 6 v h in 2 p p a on here is the density of the fluid 0 its dynamic viscosity h h x is the distance between the two bodies and p a 0 is the given ambient pressure we will assume all along that h is a lipschitz continuous function such that 3 0 h 1 h x h 2 a e x x y 4 h x ha e x x y where h 1 h 2 h are positive constants when the fluid is incompressible i e is a positive constant existence and uniqueness for a solution to 1 2 is a trivial matter since the equation is linear in the compressible case when 5 p the problem becomes more challenging the paper is organized as follows in section 1 we investigate the problem of existence of a solution for 1 2 when is given by 5 in section 2 we consider a case where 1 2 reduces to a one dimensional problem and we study the question of uniqueness as well as the shape of the solution finally in a third section we give some extensions of the results of section 2 in higher dimension

a ratio ergodic theorem in archimedean riesz spaces in this paper which can be thought of as a continuation of our previous article on several types of convergence and divergence in archimedean riesz spaces we extend the ornstein ratio ergodic theorem to a class of archimedean riesz spaces let e be an archimedean riesz space let be the dedekind completion of e we may and do think of e as being a riesz subspace of and let t e e be a positive linear operator let u e u 0 let i t u be the ideal in generated by the set tnu n n 0 and let i00 t u be the riesz space of all order continuous linear functionals on i t u we say that u has property p if i00 t u separates the points of i t u now let g e 0 g 0 and set un i 0n ti vn i 0n tig for every n n 0 let b be the projection band in generated by the set tng n n 0 let bd b be the band of total ratio individual divergence of the sequence un vn n n 0 with respect to b and assume that g has property p the main result of the paper is that if the sequence un vn n n 0 does not ratio converge individually on b then for every u bd b u 0 there exist v b u v 0 and a sequence of modifications n n n of g such that n n n diverges individually to on b v where b u and b v are the bands in generated by the singletons u and v respectively

quadratic variation for a class of l log l bounded two parameter martingales let m m t t in lbrack 0 1 rbrack 2 be a two parameter l log l bounded not necessarily continuous martingale assume that the marginal filtrations in the first and second directions are quasi left continuous we prove the existence of quadratic variation in the sense of convergence in probability this is done first for bounded martingales the extension to the general case is obtained by approximating a given martingale by its bounded truncations and using a two parameter version of the square function inequality of burkholder

remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions abstract in this note we present some uniqueness and comparison results for a class of problem of the form 0 1 l u h x u u h x u h 0 1 l where r n n 2 is a bounded domain l is a general elliptic second order linear operator with bounded coefficients and h is allowed to have a critical growth in the gradient in some cases our assumptions prove to be sharp

a priori estimates and bifurcation of solutions for an elliptic equation with semidefinite critical growth in the gradient abstract we study nonnegative solutions of the boundary value problem p u c x u x u 2 h x u h 0 1 l where is a smooth bounded domain of r n c l h l r for some r n 2 and c h 0 our main motivation is to study the semidefinite case namely unlike in previous work on the subject we do not assume to be uniformly positive in nor even positive everywhere in space dimensions up to n 5 we establish uniform a priori estimates for weak solutions of p when 0 is bounded away from 0 this is proved under the assumption that the supports of and c intersect a condition that we show to be actually necessary and in some cases we further assume that is uniformly positive on the support of c and or some other conditions as a consequence of our a priori estimates assuming that p 0 has a solution we deduce the existence of a continuum c of solutions such that the projection of c onto the axis is an interval of the form 0 a for some a 0 and that the continuum c bifurcates from infinity to the right of the axis 0 in particular for each 0 small enough problem p has at least two distinct solutions

on one parameter proofs of almost sure convergence of multiparameter processes the martingale convergence theorem of r cairoli 4 was proved assuming that the filtration satisfies a conditional independence assumption usualy called f4 it belongs to the folklore of the subject see also 17 that f4 can be restated as a condition on commutation of conditional expectation operators this formulation will allow us to derive cairoli s theorem from a simple general argument about operators on orlicz spaces the advantage is that one obtains a unified proof of multi parameter versions of several other results the theorems of rota dunford schwartz akcoglu and stein h fnlmer was able to apply proposition 2 1 below to random fields

existence and uniqueness of solutions to a quasilinear parabolic equation with quadratic gradients in financial markets a quasilinear parabolic equation with quadratic gradient terms is analyzed the equation models an optimal portfolio in so called incomplete financial markets consisting of risky assets and non tradable state variables its solution allows to compute an optimal portfolio strategy the quadratic gradient terms are essentially connected to the assumption that the so called relative risk aversion function is not logarithmic the existence of weak global in time solutions in any dimension is shown under natural hypotheses the proof is based on the monotonicity method of frehse furthermore the uniqueness of solutions is shown under a smallness condition on the derivatives of the covariance diffusion matrices using a nonlinear test function technique developed by barles and murat finally the influence of the non tradable state variables on the optimal value function is illustrated by a numerical example in three dimensions

backward stochastic partial differential equations with quadratic growth abstract this paper is concerned with the weak solution in analytic sense to the cauchy dirichlet problem of a backward stochastic partial differential equation when the nonhomogeneous term has a quadratic growth in both the gradient of the first unknown and the second unknown existence and uniqueness results are obtained under separate conditions

some qualitative properties of solutions of quasilinear elliptic equations and applications abstract we study quasilinear elliptic equations of leray lions type in w 1 p maximum principles nonexistence and existence of solutions the control of lower upper bound for essential supremum essential infimum of solutions sign changing solutions local and global oscillation of solutions geometry of domain generating singularities of solutions and lower bounds on constants appearing in schauder agmon douglis and nirenberg estimates

uniqueness for elliptic problems with locally lipschitz continuous dependence on the solution abstract we consider a class of elliptic equations of the type div a x u u f div g with dirichlet boundary conditions and with f belonging to l 1 using the framework of renormalized solutions we prove the uniqueness of a solution when the usual lipschitz condition on the function a is relaxed

neumann problems for nonlinear elliptic equations with l 1 data abstract in the present paper we prove existence results for solutions to nonlinear elliptic neumann problems whose prototype is p u div c x u p 2 u f in u p 2 u c x u p 2 u n 0 on when f is just a summable function our approach also allows us to prove a stability result for renormalized solutions and an existence result for operator with a zero order term

nonlinear fractional laplacian problems with nonlocal gradient terms let n 2 be a smooth bounded domain for s 1 2 1 we consider a problem of the form where 0 is a real parameter f belongs to a suitable lebesgue space and is a nonlocal gradient square term given by depending on the real parameter 0 we derive existence and non existence results the proof of our existence result relies on sharp calderon zygmund type regularity results for the fractional poisson equation with low integrability data we also obtain existence results for related problems involving different nonlocal diffusion terms

existence and comparison of maximal and minimal solutions for pseudomonotone elliptic problems in l 1 we consider the nonhomogeneous dirichlet problem div a x u u f in u w on where div a x u u is a pseudomonotone operator of leray lions type defined in w1 p0 w w1 p and f is in l1 under suitable assumptions of locally lipschitz or locally holder continuity of a x s with respect to s we prove the existence of maximal and minimal renormalized solutions and comparison results with respect to data f and w the results include examples of nonmonotone operators of p laplace type for any p 1 for which it is known that uniqueness of solutions does not hold

elliptic problems with a hardy potential and critical growth in the gradient non resonance and blow up results abstract in this article we analyze existence and nonexistence of positive solutions to problem p u u 2 u x 2 f in u 0 on the main results are the following i if the quadratic term in the gradient appears in the equation as a reaction term u 2 and 0 then there is no solution to problem p even in a very weak sense ii if the quadratic term in the gradient appears in the equation as an absorption term u 2 then there exists a positive solution to p for all 0 and f l 1

uniqueness results for nonlinear elliptic equations with a lower order term abstract we prove the uniqueness of the weak solution of noncoercive nonlinear elliptic problems whose model is u w 0 1 p div a x 1 u 2 p 2 2 u b x 1 u 2 1 2 f in d where is a bounded open subset of r n n 2 p satisfies p 2 n n 1 a is a function belonging to l such that a x 0 f belongs to the dual space w 1 p b belongs to some lebesgue space l r with r r n p and belongs to the interval 0 n p r with n p r and r n p functions which are specified below

existence and non existence of solutions to elliptic equations with a general convection term in this paper we consider the nonlinear elliptic problem u u g u h x in u 0 on where is a smooth bounded domain of n 0 g is an arbitrary c 1 increasing function and h c 1 is non negative we completely analyse the existence and non existence of positive classical solutions in terms of the parameter we show that there exist solutions for every when 0 and the integral 1 g s d s or when 0 and the integral s g s d s conversely when the respective integrals converge and h is non trivial on existence depends on the size of moreover non existence holds for large our proofs mainly rely on comparison arguments and on the construction of suitable supersolutions in annuli our results include some cases where the function g is superquadratic and existence still holds without assuming any smallness condition on

on multiparameter ergodic and martingale theorems in infinite measure spaces a unified proof is given of several ergodic and martingale theorems in infinite measure spaces

multiparameter ratio ergodic theorems for semigroups abstract after one parameter treatment of ratio ergodic theorems for semigroups we formulate the sucheston a e convergence principle of continuous parameter type this principle plays an effective role in proving some multiparameter generalizations of chacon s type continuous ratio ergodic theorems for semigroups and of jacobs type continuous random ratio ergodic theorems for quasi semigroups in addition a continuous analogue of the brunel dunford schwartz ergodic theorem is given of sectorially restricted averages for a commutative family of semigroups we also formulate a local a e convergence principle of sucheston s type the local convergence principle is effective in proving multiparameter local ergodic theorems in fact a multiparameter generalization of akcoglu chacon s local ratio ergodic theorem for semigroups of positive linear contractions on l 1 is proved moreover some multiparameter martingale theorems are obtained as applications of convergence principles

solvability of uniformly elliptic fully nonlinear pde we get existence uniqueness and non uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of the hamilton jacobi bellman isaacs type with unbounded ingredients and quadratic growth in the gradient without hypotheses of convexity or properness some of our results are new even for equations in divergence form

comparison principle for some classes of nonlinear elliptic equations abstract we prove a comparison principle for second order quasilinear elliptic operators in divergence form when a first order term appears we deduce uniqueness results for weak solutions to dirichlet problems when data belong to the natural dual space

two parameter optimal stopping and bi markov processes in this paper the optimal stopping problem is solved for particular two parameter processes here called bi markov processes a subsequent potential theory is developed with respect to a pair of one parameter semi groups we introduce a new notion of harmonicity for two variable functions and we interpret it in the framework of the theory of bi markov processes

existence and nonexistence of solutions for singular quadratic quasilinear equations we study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient whose model is 8

very singular solutions for linear dirichlet problems with singular convection terms abstract we study the existence of distributional solutions for the boundary value problems 1 1 and 1 2 if e does not belong to l n namely e a x a r the size of a plays an important role if n 2 a n 1 we prove that if f l 1 there exists a distributional solution u w 0 1 q for every q n a n n 1 of 1 1 the case a n 2 is studied in boccardo 2015 we then use this result to prove the existence of a bounded weak solution of 1 2 if g x l m m n n a n 2

backwards sde with random terminal time and applications to semilinear elliptic pde suppose im t is the filtration induced by a wiener process w in r d tau is a finite im t stopping time terminal time xi is an im tau measurable random variable in r k terminal value and f cdot y z is a coefficient process depending on y in r k and z in l r d r k satisfying y tilde y f s y z f s tilde y z leq a y tilde y 2 f need not be lipschitz in y and f s y z f s y tilde z leq b z tilde z for some real a and b plus other mild conditions we identify a hilbert space depending on tau and on the number gamma equiv b 2 2a in which there exists a unique pair of adapted processes y z satisfying the stochastic differential equation dy s 1 s leq tau z s dw s f s y s z s ds with the given terminal condition y tau xi provided a certain integrability condition holds this result is applied to construct a continuous viscosity solution to the dirichlet problem for a class of semilinear elliptic pde s

two parameter hunt processes and a potential theory on considere un processus de markov a deux parametres a deux trajectoires regulieres associe a une paire de semi groupes de feller commutants p 1 et p 2 sur le meme espace e

orthogonal stochastic duality functions from lie algebra representations we obtain stochastic duality functions for specific markov processes using representation theory of lie algebras the duality functions come from the kernel of a unitary intertwiner between representations which provides generalized orthogonality relations for the duality functions in particular we consider representations of the heisenberg algebra and mathfrak su 1 1 both cases lead to orthogonal self duality functions in terms of hypergeometric functions for specific interacting particle processes and interacting diffusion processes

uniqueness of renormalized solutions of degenerate elliptic parabolic problems we consider a general class of degenerate elliptic paraboic problems associated with the equation b v t div a v dv f using kruzhkov s method of doubling variables both in space and time we prove uniqueness and a comparison principle in l 1 for renormalized solutions

on optimization problems with prescribed rearrangements on considere certains resultats concernant des fonctions avec des distributions imposees et des prroblemes d optimisation qui y sont relies

some remarks on elliptic problems with critical growth in the gradient abstract in this work we analyze existence nonexistence multiplicity and regularity of solution to problem 1 u u u 2 f x in u 0 on where is a continuous nondecreasing positive function and f belongs to some suitable lebesgue spaces

uniqueness of discrete solutions of nonmonotone pdes without a globally fine mesh condition uniqueness of the finite element solution for nonmonotone quasilinear problems of elliptic type is established in one and two dimensions in each case we prove a comparison theorem based on locally bounding the variation of the discrete solution over each element the uniqueness follows from this result and does not require a globally small meshsize

coupling coefficients for lie algebra representations and addition formulas for special functions representations of the lie algebra su 1 1 and of a generalization of the oscillator algebra b 1 are considered the paper then introduces polynomials which are related by the coupling or clebsch gordan coefficients of the lie algebra in question by making a proper choice these polynomials themselves are related to known special functions the coupling of two or three representations of the lie algebra then leads to interesting addition formulas for these special functions the polynomials appearing here are generalized laguerre and jacobi polynomials for the su 1 1 case and hermite polynomials for the b 1 algebra

backward stochastic differential equations and partial differential equations with quadratic growth we provide existence comparison and stability results for one dimensional backward stochastic differential equations bsdes when the coefficient or generator f t y z is continuous and has a quadratic growth in z and the terminal condition is bounded we also give in this framework the links between the solutions of bsdes set on a diffusion and viscosity or sobolev solutions of the corresponding semilinear partial differential equations