×

zbMATH — the first resource for mathematics

Existence of bounded solutions to some nonlinear degenerate elliptic systems. (English) Zbl 1159.35337
Summary: We prove existence of bounded weak solutions \(u:\Omega\subset\mathbb R^n\to\mathbb R^N\) for the Dirichlet problem
\[ \begin{aligned} -\operatorname{div} (a(x,u(x),Du(x)))= f(x), &\quad x\in\Omega,\\ u(x)=0, &\quad x \in \partial\Omega\end{aligned} \]
where \(\Omega\) is a bounded open set, \(a\) is a suitable degenerate elliptic operator and \(f\) has enough integrability.

MSC:
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35J60 Nonlinear elliptic equations
35J70 Degenerate elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
PDF BibTeX XML Cite
Full Text: DOI