Poincaré inequalities for powers and products of admissible weights.
Regularity at infinity for a mixed problem for degenerate elliptic operators in a half-cylinder.
Mappings with dilatation in Orlicz spaces.
Approximations by regular sets and Wiener solutions in metric spaces
Let be a complete metric space equipped with a doubling Borel measure supporting a weak Poincaré inequality. We show that open subsets of can be approximated by regular sets. This has applications in nonlinear potential theory on metric spaces. In particular it makes it possible to define Wiener solutions of the Dirichlet problem for -harmonic functions and to show that they coincide with three other notions of generalized solutions.
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