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# 東工大 数理解析セミナー： Dorin Bucur 氏

2019年7月12日（金）

17:00～18:30

Dorin Bucur 氏（Université de Savoie）

Spectral isoperimetric inequalities for the Robin Laplacian

アブストラクト
Optimal constants in Poincaré inequalities with traces, Faber-Krahn and Saint-Venant inequalities for the Robin-Laplacian, all of them involve a control of some $L^q$-norm of a function $u \in W^{1,p}(\Omega)$ in terms of the $L^p$-norm of the gradient and some $L^s$-norm of the trace of $u$ on $\partial \Omega$. The optimal constant is not only sharp, but it is also independent on the geometry of the domain $\Omega$. Quite often, these kind of optimal inequalities can be set in terms of shape optimization problems for eigenvalues. In this talk, I will start with a survey of recent results involving spectral isoperimetric inequalities for the eigevalues of the Laplace operator. Then, I will focus on some new results involving the Robin-Laplacian and finally I will show how to prove the quantitative Faber-Krahn inequality by free discontinuity methods.