Shape optimisation problems governed by nonlinear state equations
Dorin Bucur, Paola Trebeschi · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1998
The purpose of this paper is to give a compactness-continuity result for the solution of a nonlinear Dirichlet problem in terms of its domain variation. The topology in the family of domains is given by the Hausdorff metric and continuity is obtained under capacity conditions. A generalisation of Sverak's result in iV-dimensions is deduced as a particular case.