Qualitative properties of the heat content

Fuente: arXiv

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Detalles Bibliográficos
Autores principales:	Berg, Michiel van den, Gittins, Katie
Formato:	Preprint
Publicado:	2024
Materias:	Analysis of PDEs
Acceso en línea:	Acceder al recurso
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

_version_	1866916700371288064
author	Berg, Michiel van den Gittins, Katie
author_facet	Berg, Michiel van den Gittins, Katie
contents	We obtain monotonicity and convexity results for the heat content of domains in Riemannian manifolds and in Euclidean space subject to various initial temperature conditions. We introduce the notion of a strictly decreasing temperature set, and show that it is a sufficient condition to ensure monotone heat content. In addition, in Euclidean space, we construct a domain and an initial condition for which the heat content is not monotone, as well as a domain and an initial condition for which the heat content is monotone but not convex.
format	Preprint
id	arxiv_https___arxiv_org_abs_2408_02447
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Qualitative properties of the heat content Berg, Michiel van den Gittins, Katie Analysis of PDEs We obtain monotonicity and convexity results for the heat content of domains in Riemannian manifolds and in Euclidean space subject to various initial temperature conditions. We introduce the notion of a strictly decreasing temperature set, and show that it is a sufficient condition to ensure monotone heat content. In addition, in Euclidean space, we construct a domain and an initial condition for which the heat content is not monotone, as well as a domain and an initial condition for which the heat content is monotone but not convex.
title	Qualitative properties of the heat content
topic	Analysis of PDEs
url	https://arxiv.org/abs/2408.02447

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