Displaying similar documents to “Limitation of solutions of parabolic equations”

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

Neil Watson (2000)

Annales Polonici Mathematici

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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...