About Three Dimensional Jump Boundary Value Problems for the Laplacian

TL;DR

This paper investigates the well-posedness of three-dimensional jump boundary value problems for the Laplacian, establishing conditions and integral equations involving layer potentials in a specialized Hilbert space.

Contribution

It provides new criteria for solvability and formulates integral equations for jump problems involving the Laplacian in three dimensions.

Findings

Conditions for well-posedness are established.

Integral equation systems for layer potentials are derived.

The analysis is conducted in a specific Hilbert space setting.

Abstract

The conditions of well-posed solvability of searched function and its normal derivative three dimensional jump problem for the Laplacian and equivalent to them integral equation system for the sum of the simple and double layer potentials are determined in the Hilbert space, element of which as well as their normal derivatives have the jump through boundary surface.