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2002 Semilinear elliptic equations and systems with measure data: existence and a priori estimates
Marie Françoise Bidaut-Véron, Cecilia Yarur
Adv. Differential Equations 7(3): 257-296 (2002). DOI: 10.57262/ade/1356651826

Abstract

We give existence results and a priori estimates for a semilinear elliptic problem of the form \begin{equation*} \left\{ \begin{array}{l} -\Delta w=w^{Q}+\mu ,\qquad \text{in \thinspace }\Omega , \\ w=\lambda ,\qquad \qquad \qquad \quad \text{on }\partial \Omega , \end{array} \right. \end{equation*} where $Q>0,$ and $\mu $ and $\lambda $ are nonnegative Radon measures in $ \Omega $ and $\partial \Omega ,$ with $\int_{\Omega }\rho \,d\mu <+\infty ,$ where $\rho $ is the distance to $\partial \Omega .$ We extend the results to the case of systems \begin{equation*} \left\{ \begin{array}{l} -\Delta u=v^{p}+\mu ,\qquad -\Delta v=u^{q}+\eta ,\qquad \text{in }\Omega , \\ u=\lambda ,\qquad v=\kappa ,\qquad \text{on }\partial \Omega , \end{array} \right. \end{equation*} with $p,q>0,$ and the same assumptions on $\eta $ and $\kappa .$

Citation

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Marie Françoise Bidaut-Véron. Cecilia Yarur. "Semilinear elliptic equations and systems with measure data: existence and a priori estimates." Adv. Differential Equations 7 (3) 257 - 296, 2002. https://doi.org/10.57262/ade/1356651826

Information

Published: 2002
First available in Project Euclid: 27 December 2012

zbMATH: 1223.35168
MathSciNet: MR1867688
Digital Object Identifier: 10.57262/ade/1356651826

Subjects:
Primary: 35J65
Secondary: 35B45 , 35R05

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.7 • No. 3 • 2002
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