entropy solutions for stochastic porous media equations we provide an entropy formulation for porous medium type equations with a stochastic non linear spatially inhomogeneous forcing well posedness and l1 contraction is obtained in the class of entropy solutions our scope allows for porous medium operators u m 1u for all m 1 and holder continuous diffusion nonlinearity with exponent 1 2

measure valued random processes measure valued random processes arise naturally in a variety of theoretical and applied settings for example marked point processes population processes measure valued diffusions and measure valued martingales related to stochastic integration they should also be useful for modelling continuum phenomena this paper undertakes a systematic study of measure valued processes and comprises three parts the first is a study of the general theory with emphasis on the compatibility between measure theoretic operations and probabilistic structure in the second part we develop the analogues of ordinary martingale theory in the measure valued situation the third part deals with measure valued processes which are increasing functions of time these are called accumulation processes a more or less complete description is given of the lebesgue decomposition of an accumulation process with respect to a fixed measure the results are used to obtain a peculiar geometrical property of markov processes and to derive a recent result of j g wendel giving the joint distribution of the hitting time and place of a sphere by brownian motion a similar result for the hitting time of the ornstein uhlenbeck process is also given

on a special type of solutions of arbitrary higher spin dirac operators in this paper an explicit expression is determined for the elliptic higher spin dirac operator acting on functions f x taking values in an arbitrary irreducible finite dimensional module for the group spin m characterized by a half integer highest weight also a special class of solutions of these operators is constructed and the connection between these solutions and transvector algebras is explained

on the representation of unity by binary cubic forms if f x y is a binary cubic form with integer coefficients such that f x 1 has at least two distinct complex roots then the equation f x y 1 possesses at most ten solutions in integers x and y nine if f has a nontrivial automorphism group if further f x y is reducible over z x y then this equation has at most 2 solutions unless f x y is equivalent under gl2 z action to either x x2 xy y2 or x x2 2y2 the proofs of these results rely upon the method of thue siegel as refined by evertse together with lower bounds for linear forms in logarithms of algebraic numbers and techniques from computational diophantine approximation along the way we completely solve all thue equations f x y 1 for f cubic and irreducible of positive discriminant df 106 as corollaries we obtain bounds for the number of solutions to more general cubic thue equations of the form f x y m and to mordell s equation y2 x3 k where m and k are nonzero integers

differential invariants and curved bernstein gelfand gelfand sequences we give a simple construction of the bernstein gelfand gelfand sequences of natural differential operators on a manifold equipped with a parabolic geometry this method permits us to define the additional structure of a bilinear differential cup product on this sequence satisfying a leibniz rule up to curvature terms it is not associative but is part of an a algebra of multilinear differential operators which we also obtain explicitly we illustrate the construction in the case of conformal differential geometry where the cup product provides a wide reaching generalization of helicity raising and lowering for conformally invariant field equations

l1 contraction and uniqueness for quasilinear elliptic parabolic equations abstract we prove the l 1 contraction principle and uniqueness of solutions for quasilinear elliptic parabolic equations of the form formula where b is monotone nondecreasing and continuous we assume only that u is a weak solution of finite energy in particular we do not suppose that the distributional derivative t b u is a bounded borel measure or a locally integrable function

universal positive mass theorems in this paper we develop a general study of contributions at infinity of bochner weitzenbock type formulas on asymptotically flat manifolds inspired by witten s proof of the positive mass theorem as an application we show that similar proofs can be obtained in a much more general setting as any choice of an irreducible natural bundle and a very large choice of first order operators may lead to a positive mass theorem along the same lines if the necessary curvature conditions are satisfied

stochastic conservation laws weak in time formulation and strong entropy condition abstract this article is an attempt to complement some recent developments on conservation laws with stochastic forcing in a pioneering development feng and nualart 8 have developed the entropy solution theory for such problems and the presence of stochastic forcing necessitates introduction of strong entropy condition however the authors formulation of entropy inequalities are weak in space but strong in time in the absence of a priori path continuity for the solutions we take a critical outlook towards this formulation and offer an entropy formulation which is weak in time and weak in space

convergence of a flux splitting finite volume scheme for conservation laws driven by levy noise abstract we explore numerical approximation of multidimensional stochastic balance laws driven by multiplicative levy noise via flux splitting finite volume method the convergence of the approximations is proved towards the unique entropy solution of the underlying problem

one dimensional stochastic burgers equation driven by levy processes abstract in this paper we proved the global existence and uniqueness of the strong weak and mild solutions for one dimensional burgers equation perturbed by a poisson form process a poisson form and q wiener process with the dirichlet bounded condition we also proved the existence of the invariant measure of these models

sharp sobolev inequalities on the sphere and the moser trudinger inequality where de denotes normalized surface measure v is the conformal gradient and q 2n n 2 a modern folklore theorem is that by taking the infinitedimensional limit of this inequality one obtains the gross logarithmic sobolev inequality for gaussian measure which determines nelson s hypercontractive estimates for the hermite semigroup see 8 one observes using conformal invariance that the above inequality is equivalent to the sharp sobolev inequality on rn for which boundedness and extremal functions can be easily calculated using dilation invariance and geometric symmetrization the roots here go back to hardy and littlewood the advantage of casting the problem on the sphere is that the role of the constants is evident and one is led immediately to the conjecture that this inequality should hold whenever possible for example 2 q 0o if n 2 this is in fact true and will be demonstrated in section 2 a clear question at this point is what is the situation in dimension 2 two important arguments 25 26 27 dealt with this issue both motivated by geometric variational problems because q goes to infinity for dimension 2 the appropriate function space is the exponential class responding in part

generalized hua operators and parabolic subgroups let g be a connected noncompact semisimple group with finite center fix g kan an iwasawa decomposition of g that is k is a maximal compact subgroup of g a a maximal vector subgroup of g with ad a consisting of semisimple elements normalizing n a maximal simply connected nilpotent subgroup of g the space 52 g k is a riemannian symmetric space and if m is the centralizer of a in k the group b man is a minimal parabolic subgroup of g and the space g b k m is called the maximal or furstenberg boundary of u2 in general a boundary of 52 will be a space of the form g p where p is some parabolic subgroup of g which we may assume contains b fixing a parabolic subgroup p of g there is a poisson kernel

branching laws for verma modules and applications in parabolic geometry i abstract we initiate a new study of differential operators with symmetries and combine this with the study of branching laws for verma modules of reductive lie algebras by the criterion for discretely decomposable and multiplicity free restrictions of generalized verma modules t kobayashi 2012 22 we are brought to natural settings of parabolic geometries for which there exist unique equivariant differential operators to submanifolds then we apply a new method f method relying on the fourier transform to find singular vectors in generalized verma modules which significantly simplifies and generalizes many preceding works in certain cases it also determines the jordan holder series of the restriction for singular parameters the f method yields an explicit formula of such unique operators for example giving an intrinsic and new proof of juhl s conformally invariant differential operators juhl 2009 16 and its generalizations to spinor bundles this article is the first in the series and the next ones include their extension to curved cases together with more applications of the f method to various settings in parabolic geometries

spinor valued l2 spaces on sm 1 and representations of spin 1 m abstract we show that the l 2 spaces of spinor valued functions on s m 1 provide models for the unitary principal series representations of spin 1 m which are characterized by the feature that they contain the fundamental spinor representation s of spin m the novelty of our approach is that we use tools characteristic of hypercomplex analysis the group spin 1 m is realized as a group of vahlen matrices and the harish chandra modules of such representations are expressed in terms of spherical monogenics which generalize the classical spherical harmonics by switching to the framework of hypercomplex analysis on the sphere we are able to extend part of the well known results for the scalar spherical principal series representations of so 1 m to the spinor setting in the process we introduce a clifford algebra valued riesz transform on the sphere

large integral points on elliptic curves to ml friend dan shanks abstract we describe several methods which permit one to search for big integral points on certain elliptic curves i e for integral solutions x of certain diophantine equations of the form v2 x3 ax b a b e z in a large range ixi iy i b in time polynomial in loglogb we also give a number of individual examples and of parametric families of examples of specific elliptic curves having a relatively large integral point

higher symmetries of the conformal powers of the laplacian on conformally flat manifolds a r g gratefully acknowledges support from the royal society of new zealand via marsden grant nos 06 uoa 029 and 10 uoa 113 j s was supported by the max planck institute fur math ematik in bonn and by the grant agency of the czech republic under the grant no p201 12 g028

an extension problem for the cr fractional laplacian we show that the conformally invariant fractional powers of the sub laplacian on the heisenberg group are given in terms of the scattering operator for an extension problem to the siegel upper halfspace remarkably this extension problem is different from the one studied among others by caffarelli and silvestre we also prove an energy identity that yields a sharp trace sobolev embedding

on the degenerate principal series of complex symplectic groups we apply techniques introduced by clerc kobayashi orsted and pevzner to study the degenerate principal series of sp n c an explicit description of the k types is provided and knapp stein normalised operators are realised as symplectic fourier transforms and their k spectrum explicitly computed reducibility phenomena are analysed in terms of k types and eigenvalues of intertwining operators we also construct a new model for these representations in which knapp stein intertwiners take an algebraic form

stochastic generalized porous media and fast diffusion equations abstract we present a generalization of krylov rozovskii s result on the existence and uniqueness of solutions to monotone stochastic differential equations as an application the stochastic generalized porous media and fast diffusion equations are studied for finite reference measures where the drift term is given by a negative definite operator acting on a time dependent function which belongs to a large class of functions comparable with the so called n functions in the theory of orlicz spaces

a discrete leading symbol and spectral asymptotics for natural differential operators we initiate a systematic study of natural differential operators in riemannian geometry whose leading symbols are not of laplace type in particular we define a discrete leading symbol for such operators which may be computed pointwise or from spectral asymptotics we indicate how this can be applied to the computation of another kind of spectral asymptotics namely asymptotic expansions of fundamental solutions and to the computation of conformally covariant operators

moser trudinger and beckner onofri s inequalities on the cr sphere we derive sharp moser trudinger inequalities on the cr sphere the rst type is in the adams form for powers of the sublaplacian and for general spectrally dened operators on the space of cr pluriharmonic functions we will then obtain the sharp beckner onofri inequality for crpluriharmonic functions on the sphere and as a consequence a sharp logarithmic hardy littlewood sobolev inequality in the form given by carlen and loss

bochner weitzenbock formulas and curvature actions on riemannian manifolds gradients are natural first order differential operators depending on riemannian metrics the principal symbols of them are related to the enveloping algebra and higher casimir elements we give formulas in the enveloping algebra that induce not only identities for higher casimir elements but also all bochner weitzenbock formulas for gradients as applications we give some vanishing theorems

on nonlinear stochastic balance laws we are concerned with multidimensional stochastic balance laws we identify a class of nonlinear balance laws for which uniform spatial bv bound for vanishing viscosity approximations can be achieved moreover we establish temporal equicontinuity in l1 of the approximations uniformly in the viscosity coefficient using these estimates we supply a multidimensional existence theory of stochastic entropy solutions in addition we establish an error estimate for the stochastic viscosity method as well as an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux and random source functions various further generalizations of the results are discussed

nonlinear fokker planck equations driven by gaussian linear multiplicative noise abstract existence of a strong solution in h 1 r d is proved for the stochastic nonlinear fokker planck equation d x div d x d t x d t x d w in 0 t r d x 0 x respectively for a corresponding random differential equation here d 1 w is a wiener process in h 1 r d d c 1 r d r d and is a continuous monotonically increasing function satisfying some appropriate sublinear growth conditions which are compatible with the physical models arising in statistical mechanics the solution exists for x l 1 l and preserves positivity if is locally lipschitz the solution is unique pathwise lipschitz continuous with respect to initial data in h 1 r d stochastic fokker planck equations with nonlinear drift of the form d x div a x d t x d t x d w are also considered for lipschitzian continuous functions a r r d

conformally invariant powers of the laplacian a complete nonexistence theorem conformally invariant operators and the equations they determine play a central role in the study of manifolds with pseudo riemannian riemannian conformai and related structures this observation dates back to at least the very early part of the last century when it was shown that the equations of massless particles on curved space time exhibit conformai invariance in this setting a key operator is the con formally invariant wave operator which has leading term a pseudo laplacian the riemannian signature variant of this operator is a fundamental tool in the yam abe problem on compact manifolds here one seeks to find a metric from a given conformai class that has constant scalar curvature recently it has become clear that higher order analogues of these operators viz conformally invariant operators on weighted functions i e conformai densities with leading term a power of the laplacian have a central role in generating and solving other curvature prescription problems as well as other problems in geometric spectral theory and mathematical physics 2 5 15 in the flat setting the existence of such operators dates back to 16 where it is shown that on 4 dimensional minkowski space for k g n 1 2 the kth power of the flat wave operator ak acting on densities of the appropriate weight is invariant under the action of the conformai group more generally if w denotes the space of conformai densities of weight uigl then on a flat conformai manifold of dimension n 3 and any signature there exists for each k e n a unique conformally invariant operator

stein weiss operators and ellipticity abstract stein and weiss 1968 am j math 90 163 196 introduced the notion of generalized gradients equivariant first order differential operators g between irreducible vector bundles with structure group so n or spin n among other things they proved ellipticity for certain systems analogous to the cauchy riemann equations and to the riemannian signature maxwell and dirac equations built from these generalized gradients in this paper we classify all systems of this type which are elliptic the answer is valid for all riemannian or if spin structure enters riemannian spin manifolds in particular we find that ellipticity may be attained by assembling surprisingly few generalized gradients the method employed yields a side benefit the spectral resolution of g g on the standard sphere s n for each generalized gradient g this spectral resolution was previously understood only for operators on small bundles for example the differential form operators d and d and the square of the dirac operator

strong solutions for stochastic partial differential equations of gradient type unique existence of analytically strong solutions to stochastic partial differential equations spde with drift given by the subdifferential of a quasi convex function and with general multiplicative noise is proven the proof applies a genuinely new method of weighted galerkin approximations based on the distance defined by the quasi convex function spatial regularization of the initial condition analogous to the deterministic case is obtained the results yield a unified framework which is applied to stochastic generalized porous media equations stochastic generalized reaction diffusion equations and stochastic generalized degenerated p laplace equations in particular higher regularity for solutions of such spde is obtained

kahlerian twistor spinors on a kahler spin manifold kahlerian twistor spinors are a natural analogue of twistor spinors on riemannian spin manifolds they are defined as sections in the kernel of a first order differential operator adapted to the kahler structure called kahlerian twistor penrose operator we study kahlerian twistor spinors and give a complete description of compact kahler manifolds of constant scalar curvature admitting such spinors as in the riemannian case the existence of kahlerian twistor spinors is related to the lower bound of the spectrum of the dirac operator

yang mills detour complexes and conformal geometry working over a pseudo riemannian manifold for each vector bundle with connection we construct a sequence of three differential operators which is a complex termed a yang mills detour complex if and only if the connection satisfies the full yang mills equations a special case is a complex controlling the deformation theory of yang mills connections in the case of riemannian signature the complex is elliptic if the connection respects a metric on the bundle then the complex is formally self adjoint in dimension 4 the complex is conformally invariant and generalises to the full yang mills setting the composition of two operator yang mills complexes for anti self dual yang mills connections via a prolonged system and tractor connection a diagram of differential operators is constructed which when commutative generates differential complexes of natural operators from the yang mills detour complex in dimension 4 this construction is conformally invariant and is used to yield two new sequences of conformal operators which are complexes if and only if the bach tensor vanishes everywhere in riemannian signature these complexes are elliptic in one case the first operator is the twistor operator and in the other sequence it is the operator for einstein scales the sequences are detour sequences associated to certain bernstein gelfand gelfand sequences

stochastic scalar conservation laws we introduce a notion of stochastic entropic solution a la kruzkov but with ito s calculus replacing deterministic calculus this results in a rich family of stochastic inequalities defining what we mean by a solution a uniqueness theory is then developed following a stochastic generalization of l1 contraction estimate an existence theory is also developed by adapting compensated compactness arguments to stochastic setting we use approximating models of vanishing viscosity solution type for the construction while the uniqueness result applies to any spatial dimensions the existence result in the absence of special structural assumptions is restricted to one spatial dimension only

group representations arising from lorentz conformal geometry abstract it is shown that there exist conformally covariant differential operators d 2 l k of all even orders 2 l on differential forms of all orders k in the double cover n of the n dimensional compactified minkowski space n these act as intertwining differential operators for natural representations of o 2 n the conformal group of n for even n the resulting decompositions of differential form representations of o 2 n the orthochronous conformal group produce infinite families of unitary representations the most interesting of which are carried by positive mass squared positive frequency quotients for 2l n 2k physically these generalize unitary representations of the conformal group associated with the modified wave operator d 2 0 n 2 2 2 and the maxwell operator on vector potentials d 2 n 2 2 d all the representation spaces produced unitary and nonunitary may be viewed as infinite systems of harmonic oscillators as a by product of the spectral resolution of the d 2 l k one gets some striking wave propagative properties for all of the equations d 2 l k 0 including huygens principle in the curved spacetime n the operators d 2 l k have not been seen before except in the special cases k 0 or n and k n 2 2 l 1 the maxwell operator thus much new information is obtained even in the physical case n 4

integer points on the curve we completely solve diophantine equations of the form y 2 x 3 p k x where k is a positive integer using a reduction to some quartic elliptic equations which can be solved with well known methods

harmonic analysis in vector bundles associated to the rotation and spin groups abstract let v be any vector bundle over the sphere s n which is associated to the principal bundle of oriented orthonormal frames or to that of spin frames we give an explicit formula for the spectrum with multiplicity of the bochner laplacian on v where is the riemannian or riemannian spin connection in the case of tensor bundles we also give the spectrum of the lichnerowicz laplacian the effect of natural first order differential operators on the corresponding eigenspaces is investigated and all results are illustrated in a detailed treatment of some examples the bundles of differential forms spinors trace free symmetric tensors and algebraic weyl tensors

bochner identities for kahlerian gradients we discuss algebraic properties for the symbols of geometric first order differential operators on kahler manifolds through a study of the universal enveloping algebra and higher casimir elements we know a lot of relations for the symbols which induce bochner identities for the operators as applications we have vanishing theorems eigenvalue estimates and so on

degenerate parabolic stochastic partial differential equations quasilinear case we study the cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical wiener process in particular we adapt the notion of kinetic formulation and kinetic solution and develop a well posedness theory that includes also an l 1 contraction property in comparison to the first order case debussche and vovelle 2010 and to the semilinear degenerate parabolic case hofmanova 2013 the present result contains two new ingredients a generalized ito formula that permits a rigorous derivation of the kinetic formulation even in the case of weak solutions of certain nondegenerate approximations and a direct proof of strong convergence of these approximations to the desired kinetic solution of the degenerate problem

hardy s inequality for fractional powers of the sublaplacian on the heisenberg group we prove hardy inequalities for the conformally invariant fractional powers of the sublaplacian on the heisenberg group h n we prove two versions of such inequalities depending on whether the weights involved are non homogeneous or homogeneous in the first case the constant arising in the hardy inequality turns out to be optimal in order to get our results we will use ground state representations the key ingredients to obtain the latter are some explicit integral representations for the fractional powers of the sublaplacian and a generalized result by m cowling and u haagerup the approach to prove the integral representations is via the language of semigroups as a consequence of the hardy inequalities we also obtain versions of heisenberg uncertainty inequality for the fractional sublaplacian c 2016 elsevier inc all rights reserved

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

stochastic nonlocal conservation laws on whole space abstract after introducing an entropy formulation for stochastic nonlocal conservation laws via an integral formula we develop a uniqueness theory by using a doubling variables technique and an existence theory by using a vanishing viscosity method we further consider the continuous dependence of the entropy solution on initial data

spectrum generating operators and intertwining operators for representations induced from a maximal parabolic subgroup abstract we present a new method of calculating intertwining operators between principal series representations of semisimple lie groups g working in the compact realization we find the eigenvalues of the operators on the k types and give several examples among the advantages of our method is its applicability to bundle valued cases

semiholonomic verma modules abstract verma modules arise geometrically through the jets of homogeneous vector bundles we consider in this article the modules that arise from the semiholonomic jets of a homogeneous vector bundle we are particularly concerned with the case of a sphere under mobius transformations in this case there are immediate applications in the theory of conformally invariant differential operators

the cos λ and sin λ transforms as intertwining operators between generalized principal series representations of sl n 1 k abstract in this article we connect topics from convex and integral geometry with well known topics in representation theory of semisimple lie groups by showing that the cos and sin transforms on the grassmann manifolds gr p k su n 1 k s u p k u n 1 p k are standard intertwining operators between certain generalized principal series representations induced from a maximal parabolic subgroup p p of sl n 1 k the index p indicates the dependence of the parabolic on p the general results of knapp and stein 1971 1980 20 21 and vogan and wallach 1990 44 then show that both transforms have meromorphic extension to c and are invertible for generic c furthermore known methods from representation theory combined with a selberg type integral allow us to determine the k spectrum of those operators

entropy solutions for nonlinear degenerate problems we consider a class of elliptic hyperbolic degenerate equations g u delta b u divg phi u f with dirichlet homogeneous boundary conditions and a class of elliptic parabolic hyperbolic degenerate equations g u t delta b u divg phi u f with homogeneous dirichlet conditions and initial conditions existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function satisfying rather general conditions comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for continuous

continuous dependence estimate for conservation laws with levy noise abstract we are concerned with multidimensional stochastic balance laws driven by levy processes using bounded variation bv estimates for vanishing viscosity approximations we derive an explicit continuous dependence estimate on the nonlinearities of the entropy solutions under the assumption that levy noise only depends on the solution this result is used to show the error estimate for the stochastic vanishing viscosity method in addition we establish fractional bv estimate for vanishing viscosity approximations in case the noise coefficient depends on both the solution and spatial variable

conformally invariant differential operators on minkowski space and their curved analogues this article describes the construction of a natural family of conformally invariant differential operators on a four dimensional pseudo riemannian manifold included in this family are the usual massless field equations for arbitrary helicity but there are many more besides the article begins by classifying the invariant operators on flat space this is a fairly straightforward task in representation theory best solved through the theory of verma modules the method generates conformally invariant operators in the curved case by means of penrose s local twistor transport

uniqueness of the bounded solution to a strongly degenerate parabolic problem abstract this paper concerns the uniqueness of the bounded solution to a strongly degenerate parabolic problem the equation considered may have two kinds of strong degeneracies and there is no restriction on the relation between the two degeneracies by using holmgren s approach we prove that the bounded solution of the associated initial boundary value problem is unique under some essentially necessary condition on the growth of the convection

laplacian operators and q curvature on conformally einstein manifolds a new definition of canonical conformal differential operators p k k 1 2 with leading term a kth power of the laplacian is given for conformally einstein manifolds of any signature these act between density bundles and more generally between weighted tractor bundles of any rank by construction these factor into a power of a fundamental laplacian associated to einstein metrics there are natural conformal laplacian operators on density bundles due to graham jenne mason sparling gjms it is shown that on conformally einstein manifolds these agree with the p k operators and hence on einstein manifolds the gjms operators factor into a product of second order laplacian type operators in even dimension n the gjms operators are defined only for 1 k n 2 and so on conformally einstein manifolds the p k give an extension of this family of operators to operators of all even orders for n even and k n 2 the operators p k are each given by a natural formula in terms of an einstein metric but they are not natural conformally invariant operators in the usual sense they are shown to be nevertheless canonical objects on conformally einstein structures there are generalisations of these results to operators between weighted tractor bundles it is shown that on einstein manifolds the branson q curvature is constant and an explicit formula for the constant is given in terms of the scalar curvature as part of development conformally invariant tractor equations equivalent to the conformal killing equation are presented

bernstein gelfand gelfand sequences the bernstein gelfand gelfand sequences extend the complexes of homogeneous vector bundles to curved cartan geometries

structure of the degenerate principal series on symmetric r spaces and small representations abstract let g be a simple real lie group with maximal parabolic subgroup p whose nilradical is abelian then x g p is called a symmetric r space we study the degenerate principal series representations of g on c x in the case where p is not conjugate to its opposite parabolic we find the points of reducibility the composition series and all unitarizable constituents among the unitarizable constituents we identify some small representations having as associated variety the minimal nilpotent k c orbit in p c where k c is the complexification of a maximal compact subgroup k g and g k p the corresponding cartan decomposition

scalar conservation laws with stochastic forcing we show that the cauchy problem for a randomly forced periodic multi dimensional scalar first order conservation law with additive or multiplicative noise is well posed it admits a unique solution characterized by a kinetic formulation of the problem which is the limit of the solution of the stochastic parabolic approximation

refined kato inequalities and conformal weights in riemannian geometry abstract we establish refinements of the classical kato inequality for sections of a vector bundle which lie in the kernel of a natural injectively elliptic first order linear differential operator our main result is a general expression which gives the value of the constants appearing in the refined inequalities these constants are shown to be optimal and are computed explicitly in most practical cases

on stochastic conservation laws and malliavin calculus abstract for stochastic conservation laws driven by a semilinear noise term we propose a generalization of the kru kov entropy condition by allowing the kru kov constants to be malliavin differentiable random variables existence and uniqueness results are provided our approach sheds some new light on the stochastic entropy conditions put forth by feng and nualart 17 and bauzet vallet and wittbold 2 and in our view simplifies some of the proofs

conformal killing forms on riemannian manifolds conformal killing forms are a natural generalization of conformal vector fields on riemannian manifolds they are defined as sections in the kernel of a conformally invariant first order differential operator we show the existence of conformal killing forms on nearly kahler and weak g2 manifolds moreover we give a complete description of special conformal killing forms a further result is a sharp upper bound on the dimension of the space of conformal killing forms

degenerate principal series representations of gln c and gln r let f be the field c or r for 1 k n 2 let pk be the maximal parabolic subgroup of gln f with its levi factor isomorphic to gln k f glk f in this paper we explicitly calculate the action of the enveloping algebra of gln f on the degenerate principal series representations induced from characters of pk we address composition series k types and unitarity