57 citations · 252 across the 40 of their papers we have counts for
5 papers · 1 filter
The Hopf-Laplace equation: harmonicity and regularity
Jan Cristina, Tadeusz Iwaniec, Leonid V. Kovalev +1
The central theme in this paper is the Hopf-Laplace equation, which represents stationary solutions with respect to the inner variation of the Dirichlet integral. Among such soluti…
Diffeomorphic approximation of Sobolev homeomorphisms
Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
Every homeomorphism h : X -> Y between planar open sets that belongs to the Sobolev class W^{1,p}(X,Y), 1<p<\infty, can be approximated in the Sobolev norm by diffeomorphisms.
Existence of energy-minimal diffeomorphisms between doubly connected domains
Tadeusz Iwaniec, Ngin-Tee Koh, Leonid V. Kovalev +1
The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Specifically, among all homeomorphisms f : R -> R* between boun…
Hopf differentials and smoothing Sobolev homeomorphisms
Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
We prove that planar homeomorphisms can be approximated by diffeomorphisms in the Sobolev space and in the Royden algebra. As an application, we show that every discrete…
Harmonic mapping problem and affine capacity
Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
The Harmonic Mapping Problem asks when there exists a harmonic homeomorphism between two given domains. It arises in the theory of minimal surfaces and in calculus of variations, s…