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Titolo:
AN UPPER ESTIMATE FOR A HEAT KERNEL WITH NEUMANN BOUNDARY-CONDITION
Autore:
LACEY AA;
Indirizzi:
HERIOT WATT UNIV,DEPT MATH EDINBURGH EH14 4AS MIDLOTHIAN SCOTLAND
Titolo Testata:
Bulletin of the London Mathematical Society
, volume: 25, anno: 1993,
parte:, 5
pagine: 453 - 462
SICI:
0024-6093(1993)25:<453:AUEFAH>2.0.ZU;2-Q
Fonte:
ISI
Lingua:
ENG
Soggetto:
FINITE-TIME BLOWUP; DOMAINS;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
CompuMath Citation Index
Science Citation Index Expanded
Citazioni:
12
Recensione:
Indirizzi per estratti:
Citazione:
A.A. Lacey, "AN UPPER ESTIMATE FOR A HEAT KERNEL WITH NEUMANN BOUNDARY-CONDITION", Bulletin of the London Mathematical Society, 25, 1993, pp. 453-462

Abstract

Using an upper solution we obtain a bound from above for the heat kernel psi(x, y, t) for a region OMEGA which is star-shaped with respect to one of the points, say y. The estimate is for the Neumann problem and holds for short times. The form of the bound is psi(x, y, t) less-than-or-equal-to (4pit)-N/2 exp[-\x - y\2/4t] + exp [-d(x, y)2/4t + O(t-1/2)]; moreover, for x is-an-element-of OMEGA\Y(y), psi(x, y, t) less-than-or-equal-to (4pit)-N/2 (exp[-\x - y\2/4t] + f(x, y) exp[-d(x, y)2/4t] (1 + O(t))). Here Y(y) is a closed subset of OMEGA subset-of R(N) with measure zero, d(x,y) is the minimum distance between x and y via the boundary partial derivative OMEGA:d(x,y) = inf(z is-an-element-of partial derivative OMEGA) (\x - z\ + \y - z\), and f(., y) is a positive function, continuous away from Y, and equal to unity on partial derivative OMEGA.

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Documento generato il 20/09/20 alle ore 04:43:57