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

Aldo Pratelli


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

Date: Jul 04, 2014, time: 11:50

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.