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Existence results for degenerate quasilinear elliptic equations in weighted Sobolev spaces. (English) Zbl 1189.35123
Summary: We are interested in the existence of solutions for Dirichlet problem associated to the degenerate quasilinear elliptic equations $$-\text{div} [v(x)\,{\cal A}(x, u, {\nabla}u)] + {\omega}(x){\cal A}_0(x,u(x))= f_0 - \sum_{j=1}^nD_jf_j, \text{ on } {\Omega}$$ in the setting of the weighted Sobolev spaces W$_0^{1,p}(\Omega,\omega,v)$. [Cf. also the editorial remark to a very similar paper in Matematiche 63, No. 2, 101--112 (2008; Zbl 1189.35124)].

35J70Degenerate elliptic equations
35J62Quasilinear elliptic equations
35D30Weak solutions of PDE
Full Text: Euclid