5 papers
Bi-Sobolev extensions
Aleksis Koski, Jani Onninen
We give a full characterization of circle homeomorphisms which admit a homeomorphic extension to the unit disk with finite bi-Sobolev norm. As a special case, a bi-conformal varian…
The Sobolev Jordan-Schonflies Problem
Aleksis Koski, Jani Onninen
We consider the planar unit disk as the reference configuration and a Jordan domain as the deformed configuration, and study the problem of extending a give…
Sobolev homeomorphic extensions onto John domains
Pekka Koskela, Aleksis Koski, Jani Onninen
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…
Radially symmetry of minimizers to the weighted Dirichlet energy
Aleksis Koski, Jani Onninen
We consider the problem of minimizing the weighted Dirichlet energy between homeomorphisms of planar annuli. A known challenge lies in the case when the weight depends on the i…
Sobolev homeomorphic extensions
Aleksis Koski, Jani Onninen
Let and be -connected Jordan domains, , with rectifiable boundaries in the complex plane. We prove that any boundary homeomorphism…