On the Laplace equation with non-local dynamical boundary conditions

TL;DR

This paper investigates non-local dynamic boundary conditions for the Laplace equation, providing analytic and probabilistic representations of solutions and interpreting them through boundary processes.

Contribution

It introduces a novel approach to analyze non-local boundary conditions for the Laplace equation using both analytic and probabilistic methods, including boundary process interpretation.

Findings

Provided compact representation of solutions

Developed probabilistic interpretation of boundary conditions

Connected boundary processes with non-local conditions

Abstract

Aim of the paper is to study non-local dynamic boundary conditions of reactive-diffusive type for the Laplace equation from analytic and probabilistic point of view. In particular, we provide compact and probabilistic representation of the solution together with an interpretation in term of boundary processes.