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arXiv · 2501.11766

Degenerate elliptic equations with $\Phi$-admissible weights

Lyudmila Korobenko
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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 Poincar\'{e} 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 $(2\sigma,2)$ Sobolev inequality with $\sigma>1$ which is typically used in the DeGiorgi or Moser iteration.

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Lyudmila Korobenko. 2025-01-20. Degenerate elliptic equations with $\Phi$-admissible weights. https://arxiv.org/abs/2501.11766

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