Monday, May 6, 2024 — 12:45 pm — laboratorio M0.2, edificio Matematica
Relationship between maximizers of maximization problems and ground state solutions of semilinear elliptic equations in $\mathbb R^2$
Abstract: We consider maximization problems in $\mathbb R^2$ with the Sobolev norm constraints and with the Dirichlet norm constraints. Typical maximization problems are the Sobolev inequalities and the Trudinger-Moser inequalities, and the existence and non-existence of maximizers for these variational problems have been studied so far. In this talk we focus on property of maximizers for the maximization problems. We show that maximizers of the maximization problems are ground state solutions of corresponding elliptic equations. In addition, we discuss the equivalence of maximizers of the maximization problems and ground state solutions of corresponding elliptic equations.