SMS scnews item created by Daniel Daners at Mon 11 Mar 2013 1353
Type: Seminar
Distribution: World
Expiry: 14 Mar 2013
Calendar1: 14 Mar 2013 1200-1300
CalLoc1: AGR Carslaw 829

PDE Seminar

Maximal regularity and applications to non-linear equations


Wolfgang Arendt
University of Ulm, Germany
14th March 2013 12:00-13:00, Carslaw Room 829 (AGR)


One of the most important applications of the celebrated De Giorgi-Nash result concerns quasi-linear elliptic equations. For quasi-linear parabolic equations one might see theorems on maximal regularity as the counterpart of the De Giorgi-Nash result. This property of maximal regularity has been investigated intensely during the last decade. We will consider mainly the case of evolution equations governed by forms.

For the applications to quasi-linear parabolic equations one needs to consider non-autonomous forms and equations. This leads to considerable difficulties since the needed form of maximal regularity is yet not known to be true (Lionsí Problem). Still, in virtue of recent results joint with Dier, Laasri and Ouhabaz we can solve a variant of Lionsí problem and are able to treat at least equation with isotropic coefficients.

Reference: W.Arendt, D. Dier, H. Laasri, E.M. Ouhabaz: Maximal regularity for evolution equations governed by non-autonomous forms, arXiv:1303.1166 (2013).

Check also the PDE Seminar page. Enquiries to Florica CÓrstea or Daniel Daners.

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