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<p>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 the related fields.</p>

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BALL-EVANS APPROXIMATION PROBLEM: RECENT PROGRESS AND OPEN PROBLEMS

  • 期刊论文

  • 发表日期：

    2025年5月23日

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  • Stanislav Hencl

摘要

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 the related fields.