On Regularity of Variational and Duality Solutions for One Class of Degenerate Elliptic Equations

P. Kogut

doi:10.15421/242604

On Regularity of Variational and Duality Solutions for One Class of Degenerate Elliptic Equations

P. Kogut (Oles Honchar Dnipro National University), https://orcid.org/0000-0003-1593-0510

Abstract

In this paper, we investigate a boundary value problem (BVP) involving a linear degenerate elliptic equation with homogeneous mixed Dirichlet-Neumann boundary conditions. Our main focus is on the cases where the weight function and its reciprocal are merely integrable, as this can lead to the Lavrent'ev gap phenomenon. We demonstrate the close relationship between the integrability of the reciprocal weight function and regularity of the variational and duality solutions of the corresponding BVP.

Keywords

degenerate elliptic equation; regularity results; variational solutions; duality solutions; weighted Sobolev spaces

MSC 2020

35J70; 35B65

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