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math.CA2021
Sobolev homeomorphic extensions from two to three dimensions
Stanislav Hencl, Aleksis Koski, Jani Onninen
We study the basic question of characterizing which boundary homeomorphisms of the unit sphere can be extended to a Sobolev homeomorphism of the interior in 3D space. While the pla…
math.AP2021
Analytic characterization of monotone Hopf-harmonics
Ilmari Kangasniemi, Aleksis Koski, Jani Onninen
We study solutions of the inner-variational equation associated with the Dirichlet energy in the plane, given homeomorphic Sobolev boundary data. We prove that such a solution is m…