Differential and Integral Equations

A free boundary problem for quasilinear elliptic equations in exterior domains

S. Carl and S. Heikkilä

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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

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

First available in Project Euclid: 30 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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