Degenerate elliptic equations with $\hat{I}¦$-admissible weights

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 $(2\ddot{I}ƒ,2)$ Sobolev inequality with $\ddot{I}ƒ>1$ which is typically used in the DeGiorgi or Moser iteration.

some typos fixed