Dirichlet problem for parabolic equations on Hilbert spaces

Anna Talarczyk

Studia Mathematica (2000)

  • Volume: 141, Issue: 2, page 109-142
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Talarczyk, Anna. "Dirichlet problem for parabolic equations on Hilbert spaces." Studia Mathematica 141.2 (2000): 109-142. <http://eudml.org/doc/216776>.

@article{Talarczyk2000,
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.},
author = {Talarczyk, Anna},
journal = {Studia Mathematica},
keywords = {existence and uniqueness; probabilistic formula},
language = {eng},
number = {2},
pages = {109-142},
title = {Dirichlet problem for parabolic equations on Hilbert spaces},
url = {http://eudml.org/doc/216776},
volume = {141},
year = {2000},
}

TY - JOUR
AU - Talarczyk, Anna
TI - Dirichlet problem for parabolic equations on Hilbert spaces
JO - Studia Mathematica
PY - 2000
VL - 141
IS - 2
SP - 109
EP - 142
AB - 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.
LA - eng
KW - existence and uniqueness; probabilistic formula
UR - http://eudml.org/doc/216776
ER -

References

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