Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-13T07:02:47.433Z Has data issue: false hasContentIssue false
  • English
  • Français

ON RATIO INEQUALITIES FOR HEAT CONTENT

Published online by Cambridge University Press:  28 January 2004

BURGESS DAVIS  and
MAJID HOSSEINI
BURGESS DAVIS
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, [email protected]
MAJID HOSSEINI
Affiliation:
Department of Mathematics, State University of New York, Suite 9, 75 South Manheim Boulevard, New Paltz, NY 12561-2443, [email protected]
Get access

Abstract

Let U be a domain, convex in $x$ and symmetric about the $y$-axis, which is contained in a centered and oriented rectangle $S$. It is proved that $H_t{(U^+)}/H_t{(U)}\,{\leq}\, H_t{(S^+)}/H_t{(S)}$ where $H_t$ stands for heat content, that is, the remaining heat in the domain at time $t$ if it initially has uniform temperature 1, with Dirichlet boundary conditions, where $A^+\,{=}\,A\,{\cap}\, \{(x,y)\,{:}\,x\,{>}\,0\}$. It is also shown that the analog of this inequality holds for some other Schrödinger operators.

Keywords

35K05 (primary)35J1060J65 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 97 - 106
Copyright
The London Mathematical Society 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)