## Differential and Integral Equations

### Existence and regularity for a class of non-uniformly elliptic equations in two dimensions

Cristina Trombetti

#### Abstract

We prove some existence and regularity results for solutions of equations in the form $-\mathrm{div}(a(x,u) \nabla u) = f$, where $a(x,s) : \Omega \times {\mathbb R} \rightarrow {\mathbb R}$ is a bounded Carath\'eodory function satisfying the inequality $a(x,s)\ge (1+|s|)^{-\theta}$ with $0 \leq \theta \leq1$ and $\Omega$ is a bounded open set of ${\mathbb R}^2$.

#### Article information

Source
Differential Integral Equations, Volume 13, Number 4-6 (2000), 687-706.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356061245

Mathematical Reviews number (MathSciNet)
MR1750046

Zentralblatt MATH identifier
0980.35054

Subjects
Primary: 35J70: Degenerate elliptic equations
Secondary: 35B45: A priori estimates

#### Citation

Trombetti, Cristina. Existence and regularity for a class of non-uniformly elliptic equations in two dimensions. Differential Integral Equations 13 (2000), no. 4-6, 687--706. https://projecteuclid.org/euclid.die/1356061245