Probabilistic approach to homogenization for a type of multivalued Dirichlet-Neumann problems

TL;DR

This paper develops a probabilistic homogenization method for multivalued Dirichlet-Neumann problems, establishing average principles for multivalued stochastic systems and applying these to homogenize complex boundary value problems.

Contribution

It introduces new average principles for multivalued stochastic differential equations and applies them to homogenize multivalued Dirichlet-Neumann problems.

Findings

Established an average principle for multivalued stochastic differential equations.

Presented an average principle for coupled forward-backward multivalued stochastic systems.

Applied the principles to successfully homogenize a class of multivalued Dirichlet-Neumann problems.

Abstract

The work is about homogenization for a type of multivalued Dirichlet-Neumann problems. First, we prove an average principle for general multivalued stochastic differential equations in the weak sense. Then for general forward-backward coupled multivalued stochastic systems, the other average principle is presented. Finally, we apply the result to a type of multivalued Dirichlet-Neumann problems and investigate its homogenization.