ERC Workshop on Existence and Regularity for Nonlinear Systems of Partial Differential Equations*

On the approximation of W^{1,1} planar homeomorphisms by diffeomorphisms.

speaker: Aldo Pratelli (Università di Pisa)

abstract: The task of approximating a homeomorphism by smooth diffeomorphisms is a quite delicate but importat one, and it has been extensively studied in the last decades. In particular, it is known, thanks to a series of papers by Iwaniec, Kovalev and Onninen, that any W^{1,p} planar homeomorphism can be approximated in the W^{1,p} norm by diffeomorphisms, but this only worked for p>1. Only very recently we have proved, in a paper with Hencl which makes use of a completely different strategy, that the same result holds true for p=1. In this talk I will describe the history of the problem and the most important results, and then I will pass to illustrate the main ideas of the construction of the above-mentioned result with Hencl.

timetable:
Fri 4 Jul, 11:50 - 12:40, Aula Dini
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