Semigroups on generalized Sobolev spaces associated with Laplacians with applications Stochastic PDEs with singular boundary conditions

TL;DR

This paper studies semigroups generated by Laplacians with singular boundary conditions on generalized Sobolev spaces and applies these results to stochastic PDEs with such boundary conditions.

Contribution

It introduces a framework for analyzing semigroups on generalized Sobolev spaces related to Laplacians with singular boundaries and applies this to stochastic PDEs.

Findings

Semigroups are well-defined on generalized Sobolev spaces for Laplacians with singular boundaries.

Applications to stochastic PDEs demonstrate the effectiveness of the framework.

Provides new tools for handling boundary singularities in stochastic PDE analysis.

Abstract

Laplacians associated with domains with singular boundary conditions and are considered together with semigroups on generalized Sobolev spaces, they generate. Applications are given to stochastic PDEs with singular boundary conditions.