3 papers
math.AP2025
Non-isoparametric Serrin domains of with connected toric boundary
Andrea Bisterzo, Shigeru Sakaguchi
We investigate the overdetermined torsion problem $\begin{cases} -Δu = 1 & \text{in}\ Ω\\ u=0 & \text{on}\ \partial Ω\\ \frac{\partial u}{\partial ν}=\text{const.} & \text{on}\ \pa…
math.AP2024
Interaction between initial behavior of temperature and the mean curvature of the interface in two-phase heat conductors
Shigeru Sakaguchi
We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media locally with different constant conductivities, where initially…
math.SP2023
Two extremum problems for Neumann eigenvalues
Lorenzo Cavallina, Kei Funano, Antoine Henrot +3
Neumann eigenvalues being non-decreasing with respect to domain inclusion, it makes sense to study the two shape optimization problems $\min\{μ_k(Ω):Ω\mbox{ convex},Ω\subset D, \}$…