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

Tongkeun Chang; Kijung Lee; Minsuk Yang

doi:10.1007/s10959-012-0444-1

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

Tongkeun Chang, Kijung Lee, Minsuk Yang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	1135-1164
Number of pages	30
Journal	Journal of Theoretical Probability
Volume	26
Issue number	4
DOIs	https://doi.org/10.1007/s10959-012-0444-1
Publication status	Published - 2013 Dec

Bibliographical note

Funding Information:
Acknowledgements The research of T. Chang was supported by National Research Foundation of Korea (NRF-2011-0028951).

Funding Information:
The research of K. Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0026232).

All Science Journal Classification (ASJC) codes

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

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10.1007/s10959-012-0444-1

Cite this

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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.",

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note = "Funding Information: Acknowledgements The research of T. Chang was supported by National Research Foundation of Korea (NRF-2011-0028951). Funding Information: The research of K. Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0026232).",

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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.

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

Abstract

Bibliographical note

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