On Sobolev and Poincaré Inequalities on Stratified Sets

2026

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DOI 10.70474/stbfwm46
Data confidence 70 medium
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Abstract

On a set Ω ⊂ ℝᴺ, composed of finitely many manifolds of various dimensions which adjoin one another in a special way, — a stratified set — we establish analogs of the Sobolev and Poincaré inequalities for functions in Sobolev type spaces in which the exponents depend on certain characteristics reflecting the internal geometric structure of Ω.