We prove a Koebe distortion theorem for the average derivative of a quasiconformal mapping between domains in the sub-Riemannian Heisenberg group H1. Several auxiliary properties of quasiconformal mappings between subdomains ...
Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the ...
In this paper, we consider mappings on uniform domains
with exponentially integrable distortion whose Jacobian determinants
are integrable. We show that such mappings can be extended to the
boundary and moreover these ...
Kow, Pu-Zhao; Larson, Simon; Salo, Mikko; Shahgholian, Henrik(Springer Science and Business Media LLC, 2022)
In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called partial balayage procedure. We also give an application to inverse scattering ...
