Ball-Evans approximation problem: recent progress and open problems
Stanislav Hencl
TL;DR
This paper reviews the recent progress and open problems in the Ball-Evans approximation problem, focusing on approximating Sobolev homeomorphisms by diffeomorphisms, highlighting recent planar results, higher-dimensional counterexamples, and unresolved questions.
Contribution
It provides an overview of recent advances, counterexamples, and open problems in the approximation of Sobolev homeomorphisms by diffeomorphisms, emphasizing planar and higher-dimensional cases.
Findings
Recent planar approximation results
Counterexamples in higher dimensions
Open problems in the field
Abstract
In this paper we give a short overview about the Ball-Evans approximation problem, i.e. about the approximation of Sobolev homeomorphism by a sequence of diffeomorphisms (or piecewise affine homeomorphisms) and we recall the motivation for this problem. We show some recent planar results and counterexamples in higher dimension and we give a number of open problems connected to this problem and related fields.
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Taxonomy
TopicsMatrix Theory and Algorithms · Mathematical functions and polynomials · Electromagnetic Scattering and Analysis