5 papers
Rigidity for two-phase overdetermined problems in
Andrea Bisterzo, Shigeru Sakaguchi
In this paper, we study rigidity phenomena associated with a class of overdetermined two-phase problems on the -dimensional sphere . Specifically, we analyze the s…
Interaction between nonlinear diffusion and mean curvature of a surface with initial discontinuities
Shigeru Sakaguchi
We consider the Cauchy problems for a class of nonlinear diffusion equations where each initial data is given by a characteristic function of an open set in the whole Euclidean…
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…
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…
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 $\min\{μ_k(Ω):Ω\mbox{ convex},Ω\subset D, \}$…