×

Existence and regularity results for some elliptic equations with degenerate coercivity. (English) Zbl 0911.35049

The authors are interested in the study of the following elliptic problem: \[ -\text{div} (a(x,u) \nabla u) = f\quad \text{in }\Omega,\qquad u = 0\quad\text{in }\partial \Omega, \] where \(\Omega\) is a bounded, open subset of \(\mathbb{R}^n\) and \(a(x,s) : \Omega \times \mathbb{R} \to \mathbb{R}\) is a Carathéodory function such that \[ {\alpha \over (1+| s|)^\theta} \leq a(x,s) \leq \beta. \] The authors prove the existence of solutions for the given problem under various assumptions on the function \(f.\)

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
35J70 Degenerate elliptic equations
PDF BibTeX XML Cite