3 papers
math.AP2025
Quantitative Resolvent and Eigenfunction Stability for the Faber-Krahn Inequality
Mark Allen, Dennis Kriventsov, Robin Neumayer
For a bounded open set with the same volume as the unit ball, the classical Faber-Krahn inequality says that the first Dirichlet eigenvalue of the…
math.AP2024
The free boundary for semilinear problems with highly oscillating singular terms
Mark Allen, Dennis Kriventsov, Henrik Shahgholian
We investigate general semilinear (obstacle-like) problems of the form , where has a singularity/jump at giving rise to a free boundary. Unlike many wor…
math.AP2021
Linear Stability Implies Nonlinear Stability for Faber-Krahn Type Inequalities
Mark Allen, Dennis Kriventsov, Robin Neumayer
For a domain and a small number , let \[ \mathcal{E}_0(Ω) = λ_1(Ω) + {\frak{T}} {\text{tor}}(Ω) = \inf_{u, w \in H^1_0(Ω)\setminus \{0\}} \fra…