English

On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity

Probability 2020-09-28 v1

Abstract

We investigate a stochastic partial differential equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by a space-time white noise. We introduce a notion of weak solution of this equation and prove its equivalence to the already known notion of mild solution.

Keywords

Cite

@article{arxiv.2009.11915,
  title  = {On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity},
  author = {Yuliya Mishura and Kostiantyn Ralchenko and Mounir Zili},
  journal= {arXiv preprint arXiv:2009.11915},
  year   = {2020}
}

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13 pages