## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Existence results for degenerate quasilinear elliptic equations in weighted Sobolev spaces

Albo Carlos Cavalheiro

#### Abstract

In this paper we are interested in the existence of solutions for Dirichlet problem associated to the degenerate quasilinear elliptic equations $$-\,{\rm div}\, [v(x)\,{\cal A}(x, u, {\nabla}u)] + {\omega}(x){\cal A}_0(x,u(x))= f_0 - \sum_{j=1}^nD_jf_j, \ \ {\rm on } \ \ {\Omega}$$ in the setting of the weighted Sobolev spaces ${\rm W}_0^{1,p}(\Omega,\omega,v)$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 1 (2010), 141-153.

Dates
First available in Project Euclid: 5 March 2010

https://projecteuclid.org/euclid.bbms/1267798504

Mathematical Reviews number (MathSciNet)
MR2656677

Zentralblatt MATH identifier
1189.35123

Subjects
Primary: 37J70 35J60: Nonlinear elliptic equations

#### Citation

Cavalheiro, Albo Carlos. Existence results for degenerate quasilinear elliptic equations in weighted Sobolev spaces. Bull. Belg. Math. Soc. Simon Stevin 17 (2010), no. 1, 141--153. https://projecteuclid.org/euclid.bbms/1267798504