Differential and Integral Equations

A free boundary problem for quasilinear elliptic equations in exterior domains

S. Carl and S. Heikkilä

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Abstract

We prove the existence of weak solutions that belong to some local Sobolev space of a quasilinear elliptic problem in an exterior domain. The free-boundary problem considered here arises from the discontinuous behavior of the nonlinearity involved. The method of upper and lower solutions, extremality results for quasilinear elliptic problems in bounded domains, gradient estimates and abstract fixed point principles in partially ordered sets are the main tools used in the proof of our main result. An application to a superlinear discontinuous elliptic problem with the p-Laplacian is given.

Article information

Source
Differential Integral Equations, Volume 11, Number 3 (1998), 409-423.

Dates
First available in Project Euclid: 30 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367341060

Mathematical Reviews number (MathSciNet)
MR1745547

Zentralblatt MATH identifier
1005.35091

Subjects
Primary: 35R35: Free boundary problems
Secondary: 35J65: Nonlinear boundary value problems for linear elliptic equations 35R05: Partial differential equations with discontinuous coefficients or data

Citation

Carl, S.; Heikkilä, S. A free boundary problem for quasilinear elliptic equations in exterior domains. Differential Integral Equations 11 (1998), no. 3, 409--423. https://projecteuclid.org/euclid.die/1367341060


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