Shigeru Sakaguchi

activity

20082026

most citedNonlinear diffusion with a bounded stationary level surface

18 citations · 55 across the 29 of their papers we have counts for

collaborators

30 papers

math.AP2026

Ellipsoidal characterization of neutral inclusions for imperfect bonding of high-conductivity type

Junyong Eom, Shota Fukushima, Yong-Gwan Ji +3

This paper concerns neutral inclusions for imperfect bonding of high-conductivity type. An inclusion, which is a bounded domain, is said to be of imperfect bonding of high-conducti…

math.AP2023

Symmetry results for some overdetermined obstacle problems

Nicola De Nitti, Shigeru Sakaguchi

We establish symmetry results for two categories of overdetermined obstacle problems: a Serrin-type problem and a two-phase problem under the overdetermination that the interface s…

math.AP2022★ 1 cited

The stationary critical points of the fractional heat flow

Nicola De Nitti, Shigeru Sakaguchi

We study the spatial critical points of the solutions $u = u (x, t)$ of the fractional heat equation. For the Cauchy problem, we show that the origin $0$ satisfies $\nabla_x u(0,t) = 0…

math.AP2022

A symmetry theorem in two-phase heat conductors

Hyeonbae Kang, Shigeru Sakaguchi

We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one medi…

math.AP2021

The principal eigenfunction of the Dirichlet Laplacian with prescribed numbers of critical points on the upper half of a topological torus

Putri Zahra Kamalia, Shigeru Sakaguchi

We consider the principal eigenvalue problem for the Laplace-Beltrami operator on the upper half of a topological torus under the Dirichlet boundary condition. We present a constru…

math.AP2021

Large time behavior of temperature in two-phase heat conductors

Hyeonbae Kang, Shigeru Sakaguchi

We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities. The large time behavior…

math.AP2020

Patterns with prescribed numbers of critical points on topological tori

Putri Zahra Kamalia, Shigeru Sakaguchi

We study the existence of critical points of stable stationary solutions to reaction-diffusion problems on topological tori. Stable nonconstant stationary solutions are often calle…

math.DG2020★ 1 cited

The double queen Dido's problem

Lorenzo Cavallina, Antoine Henrot, Shigeru Sakaguchi

This paper deals with a variation of the classical isoperimetric problem in dimension $N \geq 2$ for a two-phase piecewise constant density whose discontinuity interface is a given h…

math.AP2020

Neutral inclusions, weakly neutral inclusions, and an over-determined problem for confocal ellipsoids

Yong-Gwan Ji, Hyeonbae Kang, Xiaofei Li +1

An inclusion is said to be neutral to uniform fields if upon insertion into a homogenous medium with a uniform field it does not perturb the uniform field at all. It is said to be…

math.AP2019

A construction of patterns with many critical points on topological tori

Putri Zahra Kamalia, Shigeru Sakaguchi

We consider reaction-diffusion equations on closed surfaces in $R^{3}$ having genus $1$ . Stable nonconstant stationary solutions are often called patterns. The purpose of thi…

math.AP2019

Polarization tensor vanishing structure of general shape: Existence for small perturbations of balls

Hyeonbae Kang, Xiaofei Li, Shigeru Sakaguchi

The polarization tensor is a geometric quantity associated with a domain. It is a signature of the small inclusion's existence inside a domain and used in the small volume expansio…

math.AP2019★ 3 cited

A characterization of a hyperplane in two-phase heat conductors

Lorenzo Cavallina, Shigeru Sakaguchi, Seiichi Udagawa

We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one has…

math.AP2019

Some characterizations of parallel hyperplanes in multi-layered heat conductors

Shigeru Sakaguchi

We consider the Cauchy problem for the heat diffusion equation in the whole space consisting of three layers with different constant conductivities, where initially the upper and m…

math.AP2018★ 3 cited

Existence of coated inclusions of general shape weakly neutral to multiple fields in two dimensions

Hyeonbae Kang, Xiaofei Li, Shigeru Sakaguchi

A two dimensional inclusion of core-shell structure is neutral to multiple uniform fields if and only if the core and the shell are concentric disks, provided that the conductivity…

math.AP2018

A simple proof of a strong comparison principle for semicontinuous viscosity solutions of the prescribed mean curvature equation

Masaki Ohnuma, Shigeru Sakaguchi

A strong comparison principle for semicontinuous viscosity solutions of the prescribed mean curvature equation is considered. The difficulties of the problem come from the fact tha…

math.AP2018★ 5 cited

Two-phase heat conductors with a surface of the constant flow property

Lorenzo Cavallina, Rolando Magnanini, Shigeru Sakaguchi

We consider a two-phase heat conductor in $R^{N}$ with $N \geq 2$ consisting of a core and a shell with different constant conductivities. We study the role played by radial…

math.AP2017★ 6 cited

Two-phase heat conductors with a stationary isothermic surface and their related elliptic overdetermined problems

Shigeru Sakaguchi

We consider a two-phase heat conductor in two dimensions consisting of a core and a shell with different constant conductivities. When the medium outside the two-phase conductor ha…

math.AP2016★ 2 cited

Two-phase heat conductors with a stationary isothermic surface

Shigeru Sakaguchi

We consider a two-phase heat conductor in $R^{N}$ with $N \geq 2$ consisting of a core and a shell with different constant conductivities. Suppose that, initially, the conduc…

math.AP2016

Symmetry problems on stationary isothermic surfaces in Euclidean spaces

Shigeru Sakaguchi

Let $S$ be a smooth hypersurface properly embedded in $R^{N}$ with $N \geq 3$ and consider its tubular neighborhood $N$ . We show that, if a heat flow over $\mathcal…

math.AP2015★ 2 cited

An over-determined boundary value problem arising from neutrally coated inclusions in three dimensions

Hyeonbae Kang, Hyundae Lee, Shigeru Sakaguchi

We consider the neutral inclusion problem in three dimensions which is to prove if a coated structure consisting of a core and a shell is neutral to all uniform fields, then the co…

math.AP2014

Stationary isothermic surfaces in Euclidean 3-space

Rolando Magnanini, Daniel Peralta-Salas, Shigeru Sakaguchi

Let $Ω$ be a domain in $R^{3}$ with $\partial Ω = \partial (R^{3} ∖ Ω)$ , where $\partial Ω$ is unbounded and connected, and let $u$ be the soluti…

math.AP2014

Interaction between fast diffusion and geometry of domain

Shigeru Sakaguchi

Let $Ω$ be a domain in $R^{N}$ , where $N \geq 2$ and $\partial Ω$ is not necessarily bounded. We consider two fast diffusion equations $\partial_t u= \mbox{div}(|\nabla u|^{p-2…

math.AP2014

When does the heat equation have a solution with a sequence of similar level sets?

Tatsuki Kawakami, Shigeru Sakaguchi

In this paper we consider the overdetermined Cauchy problem for the heat equation. We prove that if the problem has a nontrivial nonnegative solution with a certain sequence of sim…

math.AP2013★ 4 cited

Solutions of elliptic equations with a level surface parallel to the boundary: stability of the radial configuration

Giulio Ciraolo, Rolando Magnanini, Shigeru Sakaguchi

Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in…