Degenerate elliptic equations with Φ-admissible weights

2025/01/20 by Lyudmila Korobenko, Korobenko, Lyudmila
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2501.11766

openalex publication_date 2025/01/20 · openalex created_date 2025/01/23 · openalex updated_date 2026/07/28

Abstract

We develop regularity theory for degenerate elliptic equations with the degeneracy controlled by a weight. More precisely, we show local boundedness and continuity of weak solutions under the assumption of a weighted Orlicz-Sobolev and Poincaré inequalities. The proof relies on a modified DeGiorgi iteration scheme, developed in arXiv:1608.01630 and arXiv:1703.00774. The Orlicz-Sobolev inequality we assume here is much weaker than the classical (2σ,2) Sobolev inequality with σ>1 which is typically used in the DeGiorgi or Moser iteration.

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