Special Session 14: The recent progress on Allen-Cahn equation, Liouville equation and critical exponent equation

Free boundary problem and Liouville equation
Angela Pistoia
Sapienza University of Roma
Italy
Co-Author(s):    
Abstract:
I show the existence of solutions with infinite mass for the Liouville equation with Dirichlet boundary conditions in a two dimensional doubly connected domain. The key ingredient in the construction is the solution of a suitable free boundary problem. The result has been obtained in collaboration with Michal Kowalczyk and Giusi Vaira.