Volume mean values of subtemperatures
Watson, Neil
Colloquium Mathematicae, Tome 84/85 (2000), p. 253-258 / Harvested from The Polish Digital Mathematics Library
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Several authors have found the characteristic mean value formula for temperatures over heat spheres. Those who derived a corresponding formula over heat balls have all chosen different mean values. In this paper we discuss an infinity of possible means over heat balls, and show that, in the wider context of subtemperatures, some are more desirable than others.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:210854 
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     author = {Neil Watson},
     title = {Volume mean values of subtemperatures},
     journal = {Colloquium Mathematicae},
     volume = {84/85},
     year = {2000},
     pages = {253-258},
     zbl = {0967.31003},
     language = {en},
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Watson, Neil. Volume mean values of subtemperatures. Colloquium Mathematicae, Tome 84/85 (2000) pp. 253-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv86i2p253bwm/

[000] [1] A. F. Beardon, Integral means of subharmonic functions, Proc. Cambridge Philos. Soc. 69 (1971), 151-152. | Zbl 0207.11004

[001] [2] W. Fulks, A mean value theorem for the heat equation, Proc. Amer. Math. Soc. 17 (1966), 6-11.

[002] [3] L. L. Helms, Introduction to Potential Theory, Wiley, New York, 1969. | Zbl 0188.17203

[003] [4] L. P. Kuptsov, Mean property for the heat-conduction equation, Mat. Zametki 29 (1981), 211-223 (in Russian); English transl.: Math. Notes 29 (1981), 110-116. | Zbl 0465.35042

[004] [5] B. Pini, Maggioranti e minoranti delle soluzioni delle equazioni paraboliche, Ann. Mat. Pura Appl. 37 (1954), 249-264.

[005] [6] T. Radó, Subharmonic Functions, Springer, Berlin, 1937. | Zbl 63.0458.05

[006] [7] E. P. Smyrnélis, Sur les moyennes des fonctions paraboliques, Bull. Sci. Math. (2) 93 (1969), 163-173. | Zbl 0203.09701

[007] [8] N. A. Watson, A theory of subtemperatures in several variables, Proc. London Math. Soc. (3) 26 (1973), 385-417. | Zbl 0253.35045

[008] [9] N. A. Watson, Green functions, potentials, and the Dirichlet problem for the heat equation, ibid. 33 (1976), 251-298. | Zbl 0336.35046

[009] [10] N. A. Watson, A convexity theorem for local mean values of subtemperatures, Bull. London Math. Soc. 22 (1990), 245-252. | Zbl 0722.35019

[010] [11] N. A. Watson, Nevanlinna's first fundamental theorem for subtemperatures, Math. Scand. 73 (1993), 49-64. | Zbl 0794.31006