The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation
Watson, Neil
Annales Polonici Mathematici, Tome 75 (2000), p. 281-287 / Harvested from The Polish Digital Mathematics Library
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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=ℝn×]0,a[. We prove a representation theorem for an arbitrary C2,1 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.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:208401 
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Watson, Neil. The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation. Annales Polonici Mathematici, Tome 75 (2000) pp. 281-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv75z3p281bwm/

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