components of the springer fiber and domino tableaux abstract consider a complex classical semisimple lie group along with the set of its nilpotent coadjoint orbits when the group is of type a the set of orbital varieties contained in a given nilpotent orbit is described a set of standard young tableaux we parameterize both the orbital varieties and the irreducible components of unipotent varieties in the other classical groups by sets of standard domino tableaux the main tools are spaltenstein s results on signed domino tableaux together with garfinkle s operations on standard domino tableaux

approximation in higher order sobolev spaces and hodge systems abstract let d 2 be an integer 1 l d 1 and be a differential l form on r d with w 1 d coefficients it was proved by bourgain and brezis 5 theorem 5 that there exists a differential l form on r d with coefficients in l w 1 d such that d d in the same work bourgain and brezis also left as an open problem the extension of this result to the case of differential forms with coefficients in the higher order space w 2 d 2 or more generally in the fractional sobolev spaces w s p with s p d we give a positive answer to this question provided that d l d 1 where is the largest positive integer such that min p d the proof relies on an approximation result interesting in its own right for functions in w s p by functions in w s p l even though w s p does not embed into l in this critical case the proofs rely on some techniques due to bourgain and brezis but the context of higher order and or fractional sobolev spaces creates various difficulties and requires new ideas and methods

hierarchical construction of bounded solutions in critical regularity spaces we construct uniformly bounded solutions for the equations divu d f and curlu d f in the critical cases f 2 l d t d r and f2 l 3 t 3 r 3 respectively criticality in this context manifests itself by the lack of a linear solution operator mapping l d 7 l 1 t d thus the intriguing aspect here is that although the problems are linear construction of their solutions is not our constructions are special cases of a general framework for solving linear equations of the form lu d f where l is a linear operator densely defined in banach space b with a closed range in a proper subspace of lebesgue space l p and with an injective dual l the solutions are realized in terms of a multiscale hierarchical representation u d p 1 jd1 uj interesting for its own sake here the uj s are constructed recursively as minimizers of ujc1d arg min u kukbc jc1krj luk p lp

new directions in harmonic analysis on l1 abstract the study of what we now call sobolev inequalities has been studied for almost a century in various forms while it has been eighty years since sobolev s seminal mathematical contributions yet there are still things we do not understand about the action of integral operators on functions this is no more apparent than in the l 1 setting where only recently have optimal inequalities been obtained on the lebesgue and lorentz scale for scalar functions while the full resolution of similar estimates for vector valued functions is incomplete the purpose of this paper is to discuss how some often overlooked estimates for the classical poisson equation give an entry into these questions to present the state of the art of what is known and to survey some open problems on the frontier of research in the area

an alternating direction method of multipliers for the numerical solution of a fully nonlinear partial differential equation involving the jacobian determinant we consider the dirichlet problem for a partial differential equation involving the jacobian determinant in two dimensions of space the problem consists in finding a vector valued function such that the determinant of its gradient is given pointwise in a bounded domain together with essential boundary conditions this problem was initially considered in dacorogna and moser ann inst h poincare anal non lineaire 7 1990 pp 1 26 and several theoretical generalizations have been derived since in this work we design a numerical algorithm for the approximation of the solution of such a problem for various kinds of boundary data the proposed method relies on an augmented lagrangian algorithm with biharmonic regularization and low order mixed finite element approximations an iterative method allows us to decouple the nonlinearity and the differential operators numerical experiments show the capabilities of the method for benchmarks and then for more demanding test problems an erratum has bee

continuous solutions for divergence type equations associated to elliptic systems of complex vector fields abstract in this paper we characterize all the distributions f d u such that there exists a continuous weak solution v c u c n with u to the divergence type equation l 1 v 1 l n v n f where l 1 l n is an elliptic system of linearly independent vector fields with smooth complex coefficients defined on r n in case where l 1 l n is the usual gradient field on r n we recover the classical result for the divergence equation proved by t de pauw and w pfeffer its proof is based on the closed range theorem and inspired by 3 and 6 in the classical case our method slightly differs from theirs by relying on the banach grothendieck theorem and introducing tools from pseudodifferential operators useful in our local setting of a system of complex vector fields with variable coefficients

on rank one convex functions that are homogeneous of degree one we show that positively 1 homogeneous rank one convex functions are convex at 0 and at matrices of rank one the result is a special case of an abstract convexity result that we establish for positively 1 homogeneous directionally convex functions defined on an open convex cone in a finite dimensional vector space from these results we derive a number of consequences including various generalizations of the ornstein l1 non inequalities most of the results were announced in c r acad sci paris ser i 349 407 409 2011

decomposition of hardy morrey spaces abstract in this paper we establish the decompositions of hardy morrey spaces in terms of atoms concentrated on dyadic cubes which have the same cancellation properties of the classical hardy spaces

on the variety of a highest weight module 1 2 let u g be the enveloping algebra of g detailed information on the primitive spectrum prim u g of u g was summarized by conjecture 7 4 of 181 here a main question was to relate prim u g with the springer correspondence parts i ii of this conjecture were established in i ii and a partial solution to iii was given in 21 sufficient e g to treat g of type a meanwhile borho and brylinski 5 have established iii for induced ideals while barbasch and vogan 1 2 have established a version of iii in which gr i i e prim u g is replaced by a certain wavefront set known to be contained in y gr 1 this last work involves some case by case analysis and gives little indication as to why the springer correspondence should arise in the study of prim u g

nucleation of instability of the meissner state of 3 dimensional superconductors this paper concerns a nonlinear partial differential system in a 3 dimensional domain involving the operator curl2 which is a simplified model used to examine nucleation of instability of the meissner state of a superconductor as the applied magnetic field reaches the superheating field we derive a priori c 2 estimates for a weak solution h the curl of the magnetic potential and determine the location of the maximal points of curlh which correspond to the nucleation of instability of the meissner state we show that if the penetration length is small the solution exhibits a boundary layer if the applied magnetic field is homogeneous curlh is maximal around the points on the boundary where the applied field is tangential to the surface

on the distributional divergence of vector fields vanishing at infinity the equation div v f has a solution v in the space of continuous vector fields vanishing at infinity if and only if f acts linearly on bv m m 1 rm the space of functions in l m m 1 rm whose distributional gradient is a vector valued measure and satisfies the following continuity condition f uj converges to zero for each sequence uj such that the measure norms of uj are uniformly bounded and uj 0 weakly in l m m 1 rm

the form boundedness criterion for the laplacian operator abstract in this paper we characterize the class of measurable functions or more generally real or complex valued distributions f such that the commutator operator c f f acting from h 1 r d to h 1 r d in other words we give a complete solution to the problem for the boundedness of the laplacian which is fundamental to quantum mechanics

solvability of the divergence equation implies john via poincare inequality abstract let r 2 be a bounded simply connected domain we show that for a fixed every p 1 the divergence equation div v f is solvable in w 0 1 p 2 for every f l 0 p if and only if is a john domain if and only if the weighted poincare inequality u x u q d x c u x q dist x q d x holds for some every q 1 this gives a positive answer to a question raised by russ 2013 in the case of bounded simply connected domains in higher dimensions similar results are proved under some additional assumptions on the domain in question

numerical godeaux surfaces with an involution minimal algebraic surfaces of general type with the smallest possible invariants have geometric genus zero and k 2 1 and are usually called numerical godeauz surfaces although they have been studied by several authors their complete classification is not known in this paper we classify numerical godeaux surfaces with an involution i e an automorphism of order 2 we prove that they are birationally equivalent either to double covers of enriques surfaces or to double planes of two different types the branch curve either has degree 10 and suitable singularities originally suggested by campedelli or is the union of two lines and a curve of degree 12 with certain singularities the latter type of double planes are degenerations of examples described by du val and their existence was previously unknown we show some examples of this new type also computing their torsion group

embeddings for a weakly differentiable functions on domains abstract we prove that the inhomogeneous estimate of vector fields on balls in r n b d k 1 u n n 1 d x n 1 n c b a u u d x for all u c b r n holds if and only if the linear constant coefficient differential operator a of order k has finite dimensional null space fdn this generalizes the gagliardo nirenberg sobolev inequality on domains and provides the local version of the analogous homogeneous embedding in full space r n d k 1 u n n 1 d x n 1 n c r n a u d x for all u c c r n r n proved by van schaftingen precisely for elliptic and cancelling ec operators building on fundamental l 1 estimates from the works of bourgain and brezis we prove that fdn strictly implies ec and discuss the contrast between homogeneous and inhomogeneous estimates on both algebraic and analytic level

quotients of products of curves new surfaces with pg 0 and their fundamental groups we construct many new surfaces of general type with q pg 0 whose canonical model is the quotient of the product of two curves by the action of a finite group g constructing in this way many new interesting fundamental groups which distinguish connected components of the moduli space of surfaces of general type we indeed classify all such surfaces whose canonical model is singular the smooth case was classified in an earlier work as an important tool we prove a structure theorem giving a precise description of the fundamental group of quotients of products of curves by the action of a finite group g

bourgain brezis inequalities on symmetric spaces of non compact type abstract let m be a global riemannian symmetric space of non compact type we prove a duality estimate for pairings of divergence free l 1 vector fields with vector fields in a critical sobolev space on m m f d v c f l 1 d v l m d v this estimate provides a remedy for the failure of a critical sobolev embedding on such symmetric spaces

an optimal sobolev embedding for l1 abstract in this paper we establish an optimal lorentz space estimate for the riesz potential acting on curl free vectors there is a constant c c d 0 such that i f l d d 1 r d r d c f l 1 r d r d for all fields f l 1 r d r d such that curl f 0 in the sense of distributions this is the best possible estimate on this scale of spaces and completes the picture in the regime p 1 of the well established results for p 1

form boundedness of the general second order differential operator we give explicit necessary and sufficient conditions for the boundedness of the general second order differential operator i j ln aij i j j 1nbj j c with real or complex valued distributional coefficients aij bj and c acting from the sobolev space w1 2 n to its dual w 1 2 n this enables us to obtain analytic criteria for the fundamental notions of relative form boundedness compactness and infinitesimal form boundedness of c with respect to the laplacian on l 2 n in particular we establish a complete characterization of the form boundedness of the schrodinger operator i a 2 q with magnetic vector potential a lloc2 n n and q d n 2006 wiley periodicals inc

gauss green theorem for weakly differentiable vector fields sets of finite perimeter and balance laws we analyze a class of weakly differentiable vector fields f w r n r n with the property that f 2 l 1 and div f is a signed radon measure these fields are called bounded divergence measure fields the primary focus of our inves tigation is to introduce a suitable notion of the normal trace of any divergence measure field f over the boundary of an arbitrary set of finite perimeter that en sures the validity of the gauss green theorem to achieve this we first establish a fundamental approximation theorem which states that given a signed radon measurethat is absolutely continuous with respect to h n 1 on r n a ny set of finite perimeter can be approximated by a family of sets with smooth boundary essentially from the measure theoretic interior of the set with respect to the mea sure kk the total variation measure we employ this approximation theorem to derive the normal trace of f on the boundary of any set of finite perimeter e as the limit of the normal traces of f on the boundaries of the approximate sets with smooth boundary so that the gauss green theorem for f holds one with these results we analyze the cauchy flux that is bounded by a nonnegative radon measure over any oriented surface i e an n 1 dimensional surface that is a part of the boundary of a set of finite perimeter and thereby develop a general mathematical formulation of the physical principle of the balance law through the cauchy flux finally we apply this framework to the derivation of systems of balance laws with measure valued source terms from the formulation of the balance law this framework also allows the recovery of cauchy entropy flux through the lax entropy inequality for entropy solutions of hyperbolic con servation laws c 2008 wiley periodicals inc

l estimates for the bar partial problem in a half planeproblem in a half plane l approche de dualite pour trouver des solutions de f est suffisante pour plusieurs problemes apparaissant en theorie h p on donne des operateurs solution qui permettent de resoudre des problemes non resolubles par la dualite

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

a new approach to counterexamples to l 1 estimates korn s inequality geometric rigidity and regularity for gradients of separately convex functions the derivation of counterexamples to l1 estimates can be reduced to a geometric decomposition procedure along rank one lines in matrix space we illustrate this concept in two concrete applications firstly we recover a celebrated and rather complex counterexample by ornstein proving the failure of korn s inequality and of the corresponding geometrically nonlinear rigidity result in l1 secondly we construct a function f 2 which is separately convex but whose gradient is not in bvloc in the sense that the mixed derivative 2f x1 x2 is not a bounded measure

a limiting case for the divergence equation we consider the equation text div mathbb y f with f a zero average function on the torus mathbb t d in their seminal paper bourgain and brezis j am math soc 16 2 393 426 2003 electronic proved the existence of a solution mathbb y in w 1 d cap l infty for a datum f in l d we extend their result to the critical sobolev spaces w s p with s 1 p d and p ge 2 more generally we prove a similar result in the scale of triebel lizorkin spaces we also consider the equation text div mathbb y f in a bounded domain varomega subject to zero dirichlet boundary condition

gagliardo nirenberg inequalities for differential forms in heisenberg groups the l 1 sobolev inequality states that for compactly supported functions u on the euclidean n space the l n n 1 norm of a compactly supported function is controlled by the l 1 norm of its gradient the generalization to differential forms due to lanzani and stein and bourgain and brezis is recent and states that a the l n n 1 norm of a compactly supported differential h form is controlled by the l 1 norm of its exterior differential du and its exterior codifferential delta u in special cases the l 1 norm must be replaced by the mathcal h 1 hardy norm we shall extend this result to heisenberg groups in the framework of an appropriate complex of differential forms

fefferman stein decomposition for q spaces and micro local quantities abstract in this paper we study the fefferman stein decomposition of q r n and give an affirmative answer to an open problem posed by essen et al 2000 one of our main methods is to characterize the structure of the predual of q r n by the micro local quantities this result indicates that the norm of the predual space of q r n depends on the micro local structure in a self correlation way

existence and uniqueness of weak solutions for a fourth order nonlinear parabolic equation in this paper we establish the existence and uniqueness of weak solutions for the initial boundary value problem of a fourth order nonlinear parabolic equation

a discrete transform and decompositions of distribution spaces abstract we study a representation formula of the form q q q for a distribution on r n this formula is obtained by discretizing and localizing a standard littlewood paley decomposition the map taking to the sequence q q with q running over the dyadic cubes in r n is called the transform the functions q and q have a particularly simple form moreover most of the familiar distribution spaces lp spaces 1 r n we also consider pointwise multipliers for the characteristic function of a domain we obtain boundedness results for a general class of domains which properly includes lipschitz domains several interpolation methods are easily analyzed via the sequence spaces for real interpolation we obtain among other things an extension to the case p 0 this in turn gives a new approach to the traditional atomic decomposition of hardy spaces

best constants for two families of higher order critical sobolev embeddings abstract in this paper we obtain the best constants in some higher order sobolev inequalities in the critical exponent these inequalities can be separated into two types those that embed into l r n and those that embed into slightly larger target spaces concerning the former we show that for k 1 n 1 n k even one has an optimal constant c k 0 such that u l c k k n k 2 u for all u c c r n the case k n was handled in shafrir 2018 meanwhile the most significant of the latter is a variation of d adams higher order inequality of j moser for r n m n and p n m there exists a 0 and optimal constant 0 0 such that exp 0 u p a for all u such that m u l p 1 where m u l p is the traditional semi norm on the space w m p

the fefferman stein decomposition for the constantin lax majda equation regularity criteria for inviscid fluid dynamics revisited the celebrated beale kato majda bkm criterion for the 3d euler equations has been updated by kozono and taniuchi by replacing the supremum with the bounded mean oscillation norm we consider this generalized criterion in an attempt to understand it more intuitively by giving an alternative explanation for simplicity we first treat the constantin lax majda clm equation t h for the vorticity in one dimension and identify a mechanism underlying the update of such an estimate we consider a fefferman stein fs decomposition for the initial vorticity 0 h 1 and how it propagates under the dynamics of the clm equation in particular we obtain a set of dynamical equations for it which reads in its simplest case 0 t 0h 0 1h 1 and 1 t 0h 1 1h 0 the equation for the second component 1 responsible for a possible logarithmic blow up is linear and homogeneous hence it remains zero if it is so initially until a stronger blow up takes place this rules out a logarithmic blo

some new surfaces with pg 0 we give families of examples of surfaces of general type x with pg 0 k2 1 double covered by surfaces t with pg 0 k2 2 in chapter 2 we classify all such constructions with t 8 giving 4 parameter families of surfaces x for which x z2 and z4 there is a complete description of surfaces with pg 0 k2 l z4 in rl there was one example s with h s z z2 in 0 p the most interesting construction is the one in chapter 3 for which x l this answers negatively the following question are all simply connected surfaces with pg 0 k2 0 rational coming from severi s conjecture these constructions were motivated by reid s conjecture that if a given fundamental group h occurs there should be examples x t z2 with x h in the appendix we give an alternative proof of a formula for the arithmetic genus of a quotient surface based on a remark of hirzebruch

a decomposition theorem for bmo and applications abstract every function having bounded mean oscillation bmo on the line is written as a sum of coefficients times normalized rational functions with the coefficients satisfying a carleson measure packing condition this decomposition theorem and related techniques are used to obtain operator norm estimates for first and second order commutators and direct and converse singular value estimates for hankel operators and products of hankel operators

a four dimensional deformation of a numerical godeaux surface a numerical godeaux surface is a surface of general type with invariants p9 q 0 and k2 1 in this paper the moduli space of a numerical godeaux surface with order two torsion is computed to be eightdimensional whether or not the moduli space of such a surface is irreducible is still unknown the surface in this paper is constructed as one member of a four parameter family of double planes there is a natural involution on the surface inherited from the double plane construction which acts on the moduli space we show that the invariant subspace is four dimensional and coincides with the family of double planes

a constructive proof of the fefferman stein decomposition of bmo rn let s vec r left left f r 1 f cdots r n f right f in h 1 left text r n text r right right subset h 1 left text r n text r n 1 right 22 1 begin gathered s vec r left vec g left g j right j 0 cdots n right in text bmo left text r n text r n 1 right sum limits j 0 n vec r j g j 0 text in bmo left text r n text r n 1 right left text r right end gathered 22 2 j 0

besov morrey spaces function space theory and applications to non linear pde this paper is devoted to the analysis of function spaces modeled on besov spaces and their applications to non linear partial differential equations with emphasis on the incompressible isotropic navier stokes system and semilinear heat equations specifically we consider the class introduced by hideo kozono and masao yamazaki of besov spaces based on morrey spaces which we call besov morrey or bm spaces we obtain equivalent representations in terms of the weierstrass semigroup and wavelets and various embeddings in classical spaces we then establish pseudo differential and para differential estimates our results cover non regular and exotic symbols although the heat semigroup is not strongly continuous on morrey spaces we show that its action defines an equivalent norm in particular homogeneous bm spaces belong to a larger class constructed by grzegorz karch to analyze scaling in parabolic equations we compare karch s results with those of kozono and yamazaki and generalize them by obtaining short time existence and uniqueness of solutions for arbitrary data with subcritical regularity we exploit pseudo differential calculus to extend the analysis to compact smooth boundaryless riemannian manifolds bm spaces are defined by means of partitions of unity and coordinate patches and intrinsically in terms of functions of the laplace operator

korn inequality on irregular domains abstract in this paper we study the weighted korn inequality on some irregular domains e g s john domains and domains satisfying quasihyperbolic boundary conditions examples regarding sharpness of the korn inequality on these domains are presented moreover we show that korn inequalities imply certain poincare inequality

infinitesimal form boundedness and trudinger s subordination for the schrodinger operator we give explicit analytic criteria for two problems associated with the schrodinger operator h q on l2 n where q d n is an arbitrary real or complex valued potential

on a class of ill posed minimization problems in image processing in this paper we show that minimization problems involving sublinear regularizing terms are ill posed in general although numerical experiments in image processing give very good results the energies studied here are inspired by image restoration and image decomposition rewriting the nonconvex sublinear regularizing terms as weighted total variations we give a new approach to perform minimization via the well known chambolle s algorithm the approach developed here provides an alternative to the well known half quadratic minimization one

lifting degree and distributional jacobian revisited let g i 0 1 s1 if g vmo we may write g ei for some vmo this is unique modulo 2 see 13 and the earlier work 14 there is no control of bmo in terms of g bmo since we always have g bmo 2 and bmo can be arbitrarily large recall however that when g bmo is sufficiently small there is a linear estimate bmo c g bmo see 13 theorem 4 14 and remark 0 2 below we are going to establish that a norm slightly stronger than g bmo does control bmo consider for 1 p 0 s 1 the fractional sobolev space ws p i equipped with its standard seminorm

sharp a priori estimates for div curl systems in heisenberg groups abstract in this paper we prove a family of inequalities for differential forms in heisenberg groups h 1 and h 2 that are the natural counterpart of a class of div curl inequalities in de rham s complex proved by lanzani stein and bourgain brezis

distributions for which div v f has a continuous solution the equation div upsilon f has a continuous weak solution in an open set u subset of r m if and only if the distribution f satisfies the following condition the f phi i converge to 0 for every sequence phi i of test functions such that the support of each i is contained in a fixed compact subset of u and in the l 1 norm phi i converges to 0 and del phi i is bounded c 2007 wiley periodicals inc

new estimates for the div curl grad operators and elliptic problems with l1 data in the whole space and in the half space abstract in this paper we study the div curl grad operators and some elliptic problems in the whole space r n and in the half space r n with n 2 we consider data in weighted sobolev spaces and in l 1

a criterion for the boundedness of singular integrals on hypersurfaces on donne des conditions geometriques sur une hypersurface de r n pour que certaines integrales singulieres sur cette hypersurface definissent des operateurs bornes sur l 2

on the f and m riesz theorem on wedges with edges of class c 1 α this work extends the classical f and m riesz theorem to measures that are boundary values of holomorphic functions defined on wedges in mathbb c n with edges that are in the class c1

a simply connected numerical campedelli surface with an involution we construct a simply connected minimal complex surface of general type with p g 0 and k 2 2 which has an involution such that the minimal resolution of the quotient by the involution is a simply connected minimal complex surface of general type with p g 0 and k 2 1 in order to construct the example we combine a double covering and mathbb q gorenstein deformation especially we develop a method for proving unobstructedness for deformations of a singular surface by generalizing a result of burns and wahl which characterizes the space of first order deformations of a singular surface with only rational double points we describe the stable model in the sense of kollar and shepherd barron of the singular surfaces used for constructing the example we count the dimension of the invariant part of the deformation space of the example under the induced mathbb z 2 mathbb z action