A stochastic partial differential equation with values in a manifold

Tadahisa Funaki*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


We investigate a certain stochastic partial differential equation which is defined on the unit interval with periodic boundary condition and takes values in a manifold. Such equation has particularly two different applications. Namely, it determines the evolution law of an interacting constrained system of continuum distributed over the unit circle, while it defines a diffusive motion of loops on a manifold. We establish the existence and uniqueness results and then show the smoothness property of the solutions. Some examples are given in the final section.

Original languageEnglish
Pages (from-to)257-288
Number of pages32
JournalJournal of Functional Analysis
Issue number2
Publication statusPublished - 1992 Nov 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis


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