[en] In this talk, we will be concerned with the symmetries of least energy nodal solutions for the Lane-Emden problem Δu = |u|ᵖ⁻²u on Ω with zero Dirichlet or Neumann boundary conditions. We will focus on the case p close to 2 and Ω a square and will show how a Lyapunov-Schmidt reduction and computer assisted proof establishes that least energy nodal solutions are odd with respect to a diagonal of the square and even with respect to the other one.
We will also discuss symmetry breaking on rectangles.
Research center :
CREMMI - Modélisation mathématique et informatique
Disciplines :
Computer science Mathematics
Author, co-author :
Troestler, Christophe ; Université de Mons > Faculté des Sciences > Service d'Analyse numérique
Language :
English
Title :
A computer assisted proof of the symmetries of least energy nodal solutions on squares
Publication date :
27 June 2019
Number of pages :
44
Event name :
Second Days Of Nonlinear Elliptic PDE in Hauts-de-France
Event place :
Calais, France
Event date :
2019
Research unit :
S835 - Analyse numérique
Research institute :
R150 - Institut de Recherche sur les Systèmes Complexes
