4 papers
Existence and stability of solutions of the Dirichlet problem for the -Poisson equation in metric measure spaces
Luis Castillo, Timo Takala
We study the Dirichlet problem for the -Poisson equation in the metric measure space setting equipped with a doubling measure and supporting a -Poincaré inequality. We p…
Solving Dirichlet problem on unbounded uniform domains by using sphericalization techniques
Riikka Korte, Sari Rogovin, Nageswari Shanmugalingam +1
Within the setting of metric spaces equipped with a doubling measure and supporting a -Poincaré inequality, establishing existence of solutions to Dirichlet problem in a bounde…
Preserving Besov (fractional Sobolev) energies under sphericalization and flattening
Anders Björn, Jana Björn, Riikka Korte +2
We introduce a new sphericalization mapping for metric spaces that is applicable in very general situations, including totally disconnected fractal type sets. For an unbounded comp…
Sharp conditions for preserving uniformity, doubling measure and Poincaré inequality under sphericalization
Riikka Korte, Sari Rogovin, Nageswari Shanmugalingam +1
We study sphericalization, which is a mapping that conformally deforms the metric and the measure of an unbounded metric measure space so that the deformed space is bounded. The go…