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Some recent results about smooth approximation of planar bi-Sobolev maps

Venerdi' 20 Maggio 2011 - Aldo Pratelli

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Venerdi' 20 maggio 2011 alle ore 12:15 in aula 2AB45 Aldo Pratelli (Universita' di Pavia) terra' un seminario dal titolo "Some recent results about smooth approximation of planar bi-Sobolev maps".

-Abstract
We will briefly discuss the most important old and recent results about the approximation of orientation-preserving planar homeomorphisms, with a particular interest in bi-Sobolev maps. Then, we will show some very recent related results, obtained together with Daneri. In particular, we will first show that a bi-Lipschitz map on the boundary of the unit square can be always smoothly extended to the whole square remaining bi-Lipschitz. And then, that it is always possible to approximate a bi-Lipschitz omeomorphisms with smooth ones, where the approximation is in the L^infty sense of the function and its inverse, plus the L^p sense of the derivative of the function and the inverse. These are the first results showing an approximation both for u and u^{-1}.

Rif. int. M. Bardi, C. Marchi, D. Vittone

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