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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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Watson N. A.

1 2000

Wyniki wyszukiwania

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