| 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 properties of maximizers for the maximization problems.
We show that maximizers of the maximization problems are ground state solutions of corresponding elliptic equations.
Moreover, we also discuss other connections between maximizers of maximization problems and ground state solutions of corresponding elliptic equations. |
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