Second Order PDEs with Dirichlet White Noise Boundary Conditions.

Zdzislaw Brzezniak, Ben Goldys, Szymon Peszat and
Francesco Russo

january, 2015

Publication type:

Paper in peer-reviewed journals

Journal:

Journal of Evolution Equations., vol. 15 (1), pp. 1-26

DOI:

10.1007/s00028-014-0246-2

HAL:

hal-00825120

arXiv:

1305.5324

Keywords :

Partial differential equations; white noise; boundary conditions; fractional Brownian motion.

Abstract:

Poisson and heat equations with white noise Dirichlet boundary conditions are considered. The existence and uniqueness of weak solutions are proved in the space of distributions. Regularity properties of solutions are established. In particular, it is shown that the solutions are smooth inside the domain, and the rate of their blow up at the boundary is calculated. A large class of noises including Wiener and fractional Wiener space time white noise, homogeneous noise, Lévy noise are considered.

BibTeX:

@article{Brz-Gol-Pes-Rus-2015,
    author={Zdzislaw Brzezniak and Ben Goldys and Szymon Peszat and 
           Francesco Russo },
    title={Second Order PDEs with Dirichlet White Noise Boundary 
           Conditions. },
    doi={10.1007/s00028-014-0246-2 },
    journal={Journal of Evolution Equations. },
    year={2015 },
    month={1},
    volume={15 (1) },
    pages={1--26},
}