On Initial-Boundary Value Problem of the Stochastic Heat Equation in Lipschitz Cylinders

Tongkeun Chang, Kijung Lee, Minsuk Yang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider the initial boundary value problem of the non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random noises. The space boundary is Lipschitz, and we impose nonzero condition on the parabolic boundary. We prove a regularity result by finding appropriate spaces for solutions and pre-assigned data in the problem. We use a collection of tools from potential theory, harmonic analysis, and probability. Some lemmas are as important as the main theorem.

Original languageEnglish
Pages (from-to)1135-1164
Number of pages30
JournalJournal of Theoretical Probability
Volume26
Issue number4
DOIs
Publication statusPublished - 2013 Dec 1

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Stochastic Heat Equation
Initial-boundary-value Problem
Lipschitz
Random Noise
Potential Theory
Harmonic Analysis
Lemma
Regularity
Derivative
Theorem

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Cite this

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On Initial-Boundary Value Problem of the Stochastic Heat Equation in Lipschitz Cylinders. / Chang, Tongkeun; Lee, Kijung; Yang, Minsuk.

In: Journal of Theoretical Probability, Vol. 26, No. 4, 01.12.2013, p. 1135-1164.

Research output: Contribution to journalArticle

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