Dorin Bucur (Université de Savoie)
is giving a seminar on Wednesday 29 October 11-12am in Room 707A
Title: About geometric domain perturbation for elliptic PDEs
Abstract: We consider the Laplace equation with Dirichlet boundary conditions on moving domains. In two dimensions of the space, Sverak proved that the solution is stable for general perturbations, provided that the number of the connected components of the complements of the variable domains remain uniformly bounded. This is related to the fact that connectedness in two dimensions implies "fatness" in the sense of capacity. We explain this relationship, and show how this can be extended in N dimensions, or to Neumann boundary value problems.
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