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Bibliographic Details
Main Author: Korobenko, Lyudmila
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2501.11766
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Table of Contents:
  • 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.