On a nonclassical boundary balue problem for the Laplace equation in a cracked domain

TL;DR

This paper studies a Laplace equation in a cracked domain with nonstandard boundary conditions, establishing existence and uniqueness of solutions relevant to flow in fractured media.

Contribution

It introduces a nonclassical boundary value problem for the Laplace equation in cracked domains and proves the existence and uniqueness of solutions in weighted Sobolev spaces.

Findings

Existence of solutions in weighted Sobolev spaces

Uniqueness of solutions for the nonclassical boundary problem

Application to modeling flow in fractured media

Abstract

We consider the Laplace equation in a cracked plane with a nonclassical boundary conditions. This problem arises as a model of the flow in the fractured media. The main result is the theorem of existence and uniqueness of a solution in weighted Sobolev spaces.