Existence and regularity of solutions for nonlinear measure data problems with general growth
The authors study the following measure data problem with general growth \[ \begin{cases} -\operatorname{div}(A(x,Du))=\mu & \text{ in } \Omega\\ \ u=0 & \text{ on } \partial\Omega \end{cases} \] where \(\Omega\subset\mathbb R^n, n\geq 2\) is a bounded domain with a Reifenberg-flat boundary and \(\mu\) is a Radone measure with finite mass. Using the technique of SOLA solutions, the authors obtain existence of distributional solutions and an optimal Calderón-Zygmund type estimate for the solutions.
scientific article; zbMATH DE number 7344810
scientific article