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The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation

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Watson N. A.

Annales Polonici Mathematici

2000

tom 75

nr 3

281-287

Let L be a second order, linear, parabolic partial differential operator, with bounded Hölder continuous coefficients, defined on the closure of the strip $X = ℝ^{n} × ]0,a[$. We prove a representation theorem for an arbitrary $C^{2,1}$ function, in terms of the fundamental solution of the equation Lu=0. Such a theorem was proved in an earlier paper for a parabolic operator in divergence form with $C^{∞}$ coefficients, but here much weaker conditions suffice. Some consequences of the representation theorem, for the solutions of Lu=0, are also presented.

Volume mean values of subtemperatures

100%

Watson N. A.

Colloquium Mathematicum

2000

tom 86

nr 2

253-258

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Colloquium Mathematicum

2 Watson N. A.

2 2000

Wyniki wyszukiwania

The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation

Volume mean values of subtemperatures