Differential and Integral Equations
- Differential Integral Equations
- Volume 11, Number 3 (1998), 409-423.
A free boundary problem for quasilinear elliptic equations in exterior domains
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.
Differential Integral Equations, Volume 11, Number 3 (1998), 409-423.
First available in Project Euclid: 30 April 2013
Permanent link to this document
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