Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

A characterization of heat balls by a mean value property for temperatures

Author(s): Noriaki Suzuki; Neil A. Watson
Journal: Proc. Amer. Math. Soc. 129 (2001), 2709-2713.
MSC (2000): Primary 31B10, 35K05
Posted: February 9, 2001
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

We discuss an inverse mean value property of solutions of the heat equation. We show that, under certain conditions, a volume mean value identity characterizes heat balls.

References:

[1]
D. Aharonov, M.M. Schiffer and L. Zalcman, `Potato kugel', Israel J. Math., 40(1981), 331-339. MR 83d:31002
[2]
Ü. Kuran, `On the mean-value property of harmonic functions', Bull London Math. Soc., 4(1972), 311-312. MR 47:8887
[3]
I. Netuka and J. Veselý, `Mean value property and harmonic functions', Classical and modern potential theory and applications (eds. K. Gowrisankaran et al), Kluwer, Dordrecht (1994), 359-398. MR 96c:31001
[4]
B. Pini, `Maggioranti e minoranti delle soluzioni delle equazioni paraboliche', Ann. Mat. Pura Appl., 37(1954)249-264. MR 16:593f
[5]
H.S. Shapiro, The Schwarz function and its generalization to higher dimensions, John Wiley & Sons, New York, 1992. MR 93g:30059
[6]
N.A. Watson, `A theory of subtemperatures in several variables', Proc. London Math. Soc., 26(1973)385-417. MR 47:3838
[7]
N.A. Watson, `Green functions, potentials, and the Dirichlet problem for the heat equation', Proc. London Math. Soc., 33(1976)251-298; Corrigendum, ibid., 37(1978)32-34. MR 58:17149
[8]
N.A. Watson, `A convexity theorem for local mean values of subtemperatures', Bull. London Math. Soc., 22(1990)245-252. MR 91b:31012

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 31B10, 35K05

Retrieve articles in all Journals with MSC (2000): 31B10, 35K05

Additional Information:

Noriaki Suzuki
Affiliation: Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan
Email: nsuzuki@math.nagoya-u.ac.jp

Neil A. Watson
Affiliation: Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand
Email: naw@math.canterbury.ac.nz

DOI: 10.1090/S0002-9939-01-05859-2
PII: S 0002-9939(01)05859-2
Keywords: Heat ball, temperature, supertemperature, mean value property, Gauss-Weierstrass kernel
Received by editor(s): July 28, 1999
Received by editor(s) in revised form: January 20, 2000
Posted: February 9, 2001
Communicated by: Albert Baernstein II
Copyright of article: Copyright 2001, American Mathematical Society

Forward Citation(s):

Information for authors on submitting citations

The following works have cited this article

D.Aharonov, M.M.Schiffer and L.Zalcman, Potato kugel, Israel J. Math. 40 (1981), 331-339.

N.A.Watson, A convexity theorem for local mean values of subtemperatures, Bull. London Math. Soc. 22 (1990), 245-252.

H.S. Shapiro, The Schwarz function and its generalization to higher dimensions, John Wiley & Sons, 1992.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google