Special Session 1: Recent Advances in Brezis-Nirenberg Problem

Multi-Bubble Analysis for the Brezis-Nirenberg Problem
Paul Laurain
University Gustave Eiffel
France
Co-Author(s):    Tobias Konig
Abstract:
In their celebrated paper, Brezis and Nirenberg showed that the behavior of the Yamabe-type equation, can vary greatly depending on the data of the problem. In particular, there exists a notion of critical potential $a$ below which no positive solution exists. We are interested in the behavior of solutions as the potential approaches the critical potential. In particular, we will see how the location and the blow-up rate of these solutions are constrained by the Robin function of the operator $\Delta + a$ This is joint work with Tobias Konig.