**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**

Auth: daners@como.maths.usyd.edu.au

### PDE Seminar

# Maximal regularity and applications to non-linear equations

### Arendt

Wolfgang Arendt

University of Ulm, Germany

14th March 2013 12:00-13:00, Carslaw Room 829 (AGR)

## Abstract

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 (Lions’
Problem). Still, in virtue of recent results joint with Dier, Laasri and Ouhabaz we
can solve a variant of Lions’ 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
Cîrstea or Daniel Daners.