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ArticleOriginal scientific text

Title

Dirichlet problem for parabolic equations on Hilbert spaces

Authors 1

Affiliations

  1. Faculty of Mathematics, Computer Science and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Abstract

We study a linear second order parabolic equation in an open subset of a separable Hilbert space, with the Dirichlet boundary condition. We prove that a probabilistic formula, analogous to one obtained in the finite-dimensional case, gives a solution to this equation. We also give a uniqueness result.

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Studia Mathematica
2000/141/2
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Pages:
109-142
Main language of publication
English
Received
1999-08-19
Accepted
2000-02-02
Published
2000
Exact and natural sciences