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MiS Preprint
20/1998
Uniqueness and maximal regularity for nonlinear elliptic systems of n-Laplace type with measure valued right hand side
Georg Dolzmann, Norbert Hungerbühler and Stefan Müller
Abstract
We prove maximal regularity for vector valued solutions $u : \Omega \to \mathbb{R}^m$ of nonlinear elliptic system of n-Laplace type $\begin{array}-div \sigma (x,u,Du)= \mu &\ in\ &D`(\Omega ),\\ u=0 & \ on\ & \partial \Omega \end{array}$ and we establish uniqueness of solutions under a few additional assumptions. In particular we prove that solutions of the system satisfy the following estimates $||u||_{BMO(\Omega;\mathbb{R}^{ca})} \leq c1, ||Du||_{L^{n,\infty}(\Omega;M^{m \times n })}\leq c2$ where the constants depend on $\partial,\Omega$, and the measure $\mu$ through its total variation. Our analysis includes unbounded domains.
