## Differential and Integral Equations

### On a class of free boundary problems of type $div(a(X) \nabla u) = -div(\chi (u)H(X))$

#### Abstract

We consider a class of two-dimensional free boundary problems of type $div(a(X) \nabla u) = -div(\chi (u)H(X))$, where $H$ is a Lipschitz vector function satisfying $div(H(X))\geq 0$. We prove that the free boundary $\partial [u>0] \cap\Omega$ is represented locally by a family of continuous functions.

#### Article information

Source
Differential Integral Equations, Volume 19, Number 5 (2006), 481-516.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356050439

Mathematical Reviews number (MathSciNet)
MR2235138

Zentralblatt MATH identifier
1212.35508

Subjects
Primary: 35R35: Free boundary problems

#### Citation

Challal, S.; Lyaghfouri, A. On a class of free boundary problems of type $div(a(X) \nabla u) = -div(\chi (u)H(X))$. Differential Integral Equations 19 (2006), no. 5, 481--516. https://projecteuclid.org/euclid.die/1356050439