On a p-Laplace type evolution equation with random variable exponent and a stochastic force

• Applicant: Professorin Dr. Aleksandra Zimmermann
• Subject Area: Mathematics
• Term: from 2014 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 259634327

We are interested in a p-Laplace type nonlinear parabolic equation with a random variable exponent and a stochastic force. Due to the random variable exponent, this problem does not fit into the framework of classical Bochner spaces and will be studied in Lebesgue and Sobolev spaces with variable exponent on a probability space. We adapt classical monotonicity methods and tools known from stochastic partial differential equations to show existence and uniqueness of weak solutions of the Dirichlet problem. Moreover we are interested in the problem of stochastic energy and in the existence of an Itô Formula for the solutions of the studied equation. We also want to investigate generalizations for Brownian motion with values in Hilbert spaces.

• DFG Programme: Research Grants