Martin Strömqvist: The Dirichlet problem in certain varying domains

Consider Poisson's equation for the p-Laplacian with Dirichlet conditions on a family of varying sets, depending on a parameter 0 < t < 1. The solution of Poisson's equation will depend on t, and our objective is to identify its limit as t tends to zero. I will present joint work with Lee and Yoo and with Karakhanyan where the varying sets are defined as the intersection of a hyper plane and a varying periodic lattice. Our methods are based on techniques from homogenization and the theory of uniform distribution.