## Differential and Integral Equations

### 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 $\Omega$ of $\mathbb{R}^{n}$. We prove a comparison result with a suitable symmetrized'' Dirichlet problem which cannot be uniformly elliptic depending on the regularity of $\partial \Omega$. Regularity results for non-uniformly elliptic equations are also given.

#### Article information

Source
Differential Integral Equations, Volume 16, Number 5 (2003), 625-639.

Dates
First available in Project Euclid: 21 December 2012