Geodesic
The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation
Annales Polonici Mathematici, Tome 75 (2000) no. 3, pp. 281-287.

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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.
DOI : 10.4064/ap-75-3-281-287
Keywords: fundamental solution, parabolic equation, representation theorem

Neil Watson 1

1 
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Neil Watson. The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation. Annales Polonici Mathematici, Tome 75 (2000) no. 3, pp. 281-287. doi : 10.4064/ap-75-3-281-287. http://geodesic.mathdoc.fr/articles/10.4064/ap-75-3-281-287/

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