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.
Bibliographical noteFunding Information:
Acknowledgements The research of T. Chang was supported by National Research Foundation of Korea (NRF-2011-0028951).
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
- Statistics, Probability and Uncertainty