Sobolev-type regularity and Pohozaev-type identities for some degenerate and singular problems

TL;DR

This paper establishes Sobolev regularity results and Pohozaev identities for solutions to degenerate and singular elliptic equations with non-homogeneous Neumann boundary conditions.

Contribution

It introduces new regularity results and Pohozaev identities for elliptic equations with singular or degenerate weights, expanding understanding of such problems.

Findings

Proved Sobolev regularity for solutions with singular/degenerate weights.

Derived a Pohozaev-type identity for weak solutions.

Applicable to elliptic equations with non-homogeneous Neumann conditions.

Abstract

Sobolev-type regularity results are proved for solutions to a class of second order elliptic equations with a singular or degenerate weight, under non-homogeneous Neumann conditions. As an application a Pohozaev-type identity for weak solutions is derived.