Movement of centers with respect to various potentials

Shigehiro Sakata

doi:10.1090/tran/6138

Movement of centers with respect to various potentials

Shigehiro Sakata

Global Education Center

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We investigate a potential with a radially symmetric and strictly decreasing kernel depending on a parameter. We regard the potential as a function defined on the upper half-space ℝ^m ×(0,+ ∞) and study some geometric properties of its spatial maximizer. To be precise, we give some sufficient conditions for the uniqueness of a maximizer of the potential and study the asymptotic behavior of the set of maximizers. Using these results, we imply geometric properties of some specific potentials. In particular, we consider applications for the solution of the Cauchy problem for the heat equation, the Poisson integral (including a solid angle) and r^α-m-potentials.

Original language	English
Pages (from-to)	8347-8381
Number of pages	35
Journal	Transactions of the American Mathematical Society
Volume	367
Issue number	12
DOIs	https://doi.org/10.1090/tran/6138
Publication status	Published - 2015 Dec 1

Keywords

Alexandrov's reflection principle
Heart
Hot spot
Illuminating center
Minimal unfolded region
Moving plane method
Newton potential
Poisson integral
Rα-m-potential
Radial center
Riesz potential
Solid angle

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/tran/6138

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abstract = "We investigate a potential with a radially symmetric and strictly decreasing kernel depending on a parameter. We regard the potential as a function defined on the upper half-space ℝm ×(0,+ ∞) and study some geometric properties of its spatial maximizer. To be precise, we give some sufficient conditions for the uniqueness of a maximizer of the potential and study the asymptotic behavior of the set of maximizers. Using these results, we imply geometric properties of some specific potentials. In particular, we consider applications for the solution of the Cauchy problem for the heat equation, the Poisson integral (including a solid angle) and rα-m-potentials.",

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N2 - We investigate a potential with a radially symmetric and strictly decreasing kernel depending on a parameter. We regard the potential as a function defined on the upper half-space ℝm ×(0,+ ∞) and study some geometric properties of its spatial maximizer. To be precise, we give some sufficient conditions for the uniqueness of a maximizer of the potential and study the asymptotic behavior of the set of maximizers. Using these results, we imply geometric properties of some specific potentials. In particular, we consider applications for the solution of the Cauchy problem for the heat equation, the Poisson integral (including a solid angle) and rα-m-potentials.

AB - We investigate a potential with a radially symmetric and strictly decreasing kernel depending on a parameter. We regard the potential as a function defined on the upper half-space ℝm ×(0,+ ∞) and study some geometric properties of its spatial maximizer. To be precise, we give some sufficient conditions for the uniqueness of a maximizer of the potential and study the asymptotic behavior of the set of maximizers. Using these results, we imply geometric properties of some specific potentials. In particular, we consider applications for the solution of the Cauchy problem for the heat equation, the Poisson integral (including a solid angle) and rα-m-potentials.

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KW - Hot spot

KW - Illuminating center

KW - Minimal unfolded region

KW - Moving plane method

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KW - Poisson integral

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KW - Radial center

KW - Riesz potential

KW - Solid angle

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