English

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

Analysis of PDEs 2025-12-16 v2

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.

Keywords

Cite

@article{arxiv.2412.10171,
  title  = {On a nonclassical boundary balue problem for the Laplace equation in a cracked domain},
  author = {Mykola Krasnoshchok},
  journal= {arXiv preprint arXiv:2412.10171},
  year   = {2025}
}