An approximation theorem in higher order Orlicz-Sobolev spaces and applications
An elementary proof of Marcellini Sbordone semicontinuity theorem
The weak lower semicontinuity of the functional is a classical topic that was studied thoroughly. It was shown that if the function is continuous and convex in the last variable, the functional is sequentially weakly lower semicontinuous on . However, the known proofs use advanced instruments of real and functional analysis. Our aim here is to present a proof understandable even for students familiar only with the elementary measure theory.
An embedding norm and the Lindqvist trigonometric functions.
An embedding theorem for a weighted space of Sobolev type and correct solvability of the Sturm-Liouville equation
An embedding theorem for Campanato spaces.
An embedding theorem for Sobolev type functions with gradients in a Lorentz space
The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.
An estimate in the spirit of Poincaré's inequality
An ill-posed nonlocal two-point problem for systems of partial differential equations.
An imbedding theorem for H°(G,Ω)-spaces
An interpolation inequality in exterior domains
An interpolation inequality involving Hölder norms.
An L...-Estimate for the gradient of extremals.
An optimal endpoint trace embedding
We find an optimal Sobolev-type space on all of whose functions admit a trace on subspaces of of given dimension. A corresponding trace embedding theorem with sharp range is established.
An optimal symbolic calculus on Besov algebras
An up-wind finite element method for a filtration problem
Analogue d'un Lemme de Kohn et Nirenberg
Analyse multi-résolution bi-orthogonale sur l'intervalle et applications
Analyses multi-résolutions non orthogonales, commutation entre projecteurs et derivation et ondelettes vecteurs à divergence nulle.
The notion of non-orthogonal multi-resolution analysis and its compatibility with differentiation (as expressed by the commutation formula) lead us to the construction of a multi-resolution analysis of L2(Rn)n which is well adapted to the approximation of divergence-free vector functions. Thus, we obtain unconditional bases of compactly supported divergence-free vector wavelets.
Analysis of the finite element method for transmission/mixed boundary value problems on general polygonal domains.
Analysis on the Heisenberg Group and Estimates for Functions in Hardy Classes of Several Complex Variables.