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.
@article{bwmeta1.element.bwnjournal-article-smv141i2p109bwm,
author = {Anna Talarczyk},
title = {Dirichlet problem for parabolic equations on Hilbert spaces},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {109-142},
zbl = {0977.35057},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv141i2p109bwm}
}
Talarczyk, Anna. Dirichlet problem for parabolic equations on Hilbert spaces. Studia Mathematica, Tome 141 (2000) pp. 109-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv141i2p109bwm/
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