### 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 language | English |
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Pages (from-to) | 1135-1164 |

Number of pages | 30 |

Journal | Journal of Theoretical Probability |

Volume | 26 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2013 Dec 1 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Journal of Theoretical Probability*,

*26*(4), 1135-1164. https://doi.org/10.1007/s10959-012-0444-1

}

*Journal of Theoretical Probability*, vol. 26, no. 4, pp. 1135-1164. https://doi.org/10.1007/s10959-012-0444-1

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - On Initial-Boundary Value Problem of the Stochastic Heat Equation in Lipschitz Cylinders

AU - Chang, Tongkeun

AU - Lee, Kijung

AU - Yang, Minsuk

PY - 2013/12/1

Y1 - 2013/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84886592914&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84886592914&partnerID=8YFLogxK

U2 - 10.1007/s10959-012-0444-1

DO - 10.1007/s10959-012-0444-1

M3 - Article

AN - SCOPUS:84886592914

VL - 26

SP - 1135

EP - 1164

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 4

ER -