Abstract
We characterize all geometric perturbations of an open set, for which the solution of a nonlinear elliptic PDE of p-Laplacian type with Dirichlet boundary condition is stable in the L ∞ -norm. The necessary and sufficient conditions are jointly expressed by a geometric property associated to the γ p -convergence. If the dimension N of the space satisfies N − 1 < p ⩽ N and if the number of the connected components of the complements of the moving domains are uniformly bounded, a simple characterization of the uniform convergence can be derived in a purely geometric frame, in terms of the Hausdorff complementary convergence. Several examples are presented.
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