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Regularity of Solutions to the Fractional Cheeger-Laplacian on Domains in Metric Spaces of Bounded Geometry
Sylvester Eriksson-Bique, Gianmarco Giovannardi, Riikka Korte +2
We study existence, uniqueness, and regularity properties of the Dirichlet problem related to fractional Dirichlet energy minimizers in a complete doubling metric measure space $(X…
Function Spaces via Fractional Poisson Kernel on Carnot Groups and Applications
Ali Maalaoui, Andrea Pinamonti, Gareth Speight
We provide a new characterization of homogeneous Besov and Sobolev spaces in Carnot groups using the fractional heat kernel and Poisson kernel. We apply our results to study commut…
Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient
Panu Lahti, Lukas Maly, Nageswari Shanmugalingam +1
We study the geometry of domains in complete metric measure spaces equipped with a doubling measure supporting a -Poincaré inequality. We propose a notion of \emph{domain with b…