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Article · St Petersburg Mathematical Journal · July 26, 2019

An analog of the Sobolev inequality on a stratified set

N. S. Dairbekov, O. M. Penkin, Lyazzat Sarybekova

Nurlan Dairbekov
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Abstract

On a set $\Omega \subset \mathbb {R}^d$ that is formed from a finite collection of manifolds that adjoin each other in a special way (i.e., on a stratified set) an exact analog of the Sobolev inequality is proved, in which the exponents are expressed via the characteristics of the intrinsic geometric structure of $\Omega$. The result is applied in order to prove the solvability of the Dirichlet problem for the $p$-Laplacian.

Nonlinear Partial Differential EquationsGeometric Analysis and Curvature FlowsAdvanced Harmonic Analysis ResearchSobolev inequalitiesstratified setsmanifolds with singularities

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