Special Session 73: Nonlinear elliptic and parabolic equations and related functional inequalities

New solutions for the Lane-Emden problem in planar domains

Luca Battaglia
Universita degli Studi Roma Tre
Italy
Co-Author(s):    Isabella Ianni, Angela Pistoia
Abstract:
We consider the Lane-Emden problem on a smooth bounded planar domain. We find nodal concentrating solutions, for large values of p, where both the positive and negative part blow up, the latter with a non-radial profile. Up to our knowledge, this is the first result concerning concentration with such a pattern for planar elliptic problems.