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2000 Existence and regularity for a class of non-uniformly elliptic equations in two dimensions
Cristina Trombetti
Differential Integral Equations 13(4-6): 687-706 (2000).

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 ${\mathbb R}^2$.

Citation

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Cristina Trombetti. "Existence and regularity for a class of non-uniformly elliptic equations in two dimensions." Differential Integral Equations 13 (4-6) 687 - 706, 2000.

Information

Published: 2000
First available in Project Euclid: 21 December 2012

zbMATH: 0980.35054
MathSciNet: MR1750046

Subjects:
Primary: 35J70
Secondary: 35B45

Rights: Copyright © 2000 Khayyam Publishing, Inc.

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Vol.13 • No. 4-6 • 2000
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