Comparison results for a linear elliptic equation with mixed boundary conditions

Abstract

In this paper we study a linear elliptic equation having mixed boundary conditions, defined in a connected open set Ω of R n. We prove a comparison result with a suitable symmetrized'' Dirichlet problem which cannot be uniformly elliptic depending on the regularity of ∂ Ω. Regularity results for non-uniformly elliptic equations are also given.