Recent Developments in Weak Convergence Methods for Nonlinear PDE

Short Course Organizer
Lawrence C Evans, Department of Mathematics, UC Berkeley

Associated SIAM Conference
SIAM Conference on Analysis of Partial Differential Equations.

Lawrence C Evans, Department of Mathematics, UC Berkeley

Course Description
In these lectures I will provide an overview of some important breakthroughs in the past decade concerning oscillations and concentration phenomena for nonlinear PDE. 

The central problem will typically be to pass to limits from approximations to exact solutions, when strong  uniform estimates are not available, and in particular to understand how this failure of strong convergence interacts with the nonlinear structure of the PDE.

Level of the Material
30% beginner
50% intermediate     
20% advanced  

Target Audience
Math faculty, advanced graduate students

Recommended Background
Basic knowledge of partial differential equations, at the level of my graduate textbook

Course Outline
Lecture 1: Overview, convexity issues
Lecture 2: Oscillations and cancellation
Lecture 3: Concentration, transport

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