**SMS scnews item created by Daniel Daners at Thu 10 Mar 2011 1439**

Type: Seminar

Distribution: World

Expiry: 14 Mar 2011

**Calendar1: 14 Mar 2011 1400-1500**

**CalLoc1: Mills Lecture Room 209**

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

### PDE Seminar

# Generalized Lax-Milgram theorem in reflexive Banach spaces and its application to elliptic boundary value problems

### Kozono

Hideo Kozono

Tohoku University, Japan

14 March 2010, 3-4pm, Mills Lecture Room 209 (note the location)

## Abstract

It is well-known that the Lax-Milgram theorem for positive definite quadratic forms on a Hilbert space is useful to show the existence of weak solutions of boundary value problems of elliptic equations. We shall generalize this theorem to the case of a one parameter family of reflexive Banach spaces. We may deal with quadratic forms which are not necessarily positive definite. Some variational inequalities play an essential role for positivity. Then we shall apply our theorem to the construction of weak solutions in Lp to a boundary value problem for an elliptic system.

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