7 papers · 1 filter
Characterizing Sobolev Homeomorphic Extensions via Internal Distances
Aleksis Koski, Jani Onninen, Haiqing Xu
We give a full characterization of embeddings of the unit circle that admit a Sobolev homeomorphic extension to the unit disk. As a direct corollary, we establish that for quasicon…
Extension of planar Hölder homeomorphisms
Stanislav Hencl, Aleksis Koski
Let \in (0; 1). We show that any -Hölder homeomorphism from the unit circle in the plane to the plane can be extended to an -Hölder homeomorphism from the whole unit disc…
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…