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2008 Existence results for non-uniformly elliptic equations with general growth in the gradient
Francesco Della Pietra
Differential Integral Equations 21(9-10): 821-836 (2008).

Abstract

We prove a priori estimates and existence results for a class of problems whose prototype is \[ -\text{div}\,(b( |{u}| ) | {Du}| ^{p-2}Du)=k( |{u} | ) |{Du}|^q+f,\quad u\in W_0^{1,p}(\Omega)\cap L^\infty(\Omega), \] where $\Omega$ is a bounded domain in $\mathbb R^n$, $p-1 < q\leq p$, and $k$ and $b$ are continuous functions.

Citation

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Francesco Della Pietra. "Existence results for non-uniformly elliptic equations with general growth in the gradient." Differential Integral Equations 21 (9-10) 821 - 836, 2008.

Information

Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35117
MathSciNet: MR2483336

Subjects:
Primary: 35J60
Secondary: 35A25, 35B45, 35J70

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.21 • No. 9-10 • 2008
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