## 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