Linear Stability Implies Nonlinear Stability for Faber-Krahn Type Inequalities

Mark Allen, Dennis Kriventsov, Robin Neumayer

For a domain $\Omega \subset {\mathbb{R}}^n$ and a small number $\mathfrak{T}>0$, let \[ \mathcal{E}_0(Ω) = λ_1(Ω) + {\frak{T}} {\text{tor}}(Ω) = \inf_{u, w \in H^1_0(Ω)\setminus \{0\}} \fra…