Fundamental solutions to elliptic equations with discontinuous senior coefficients and an inequlity for these solutions

TL;DR

This paper derives an asymptotic formula for the fundamental solution of elliptic operators with discontinuous coefficients, providing insights useful for inverse problems involving such operators.

Contribution

It introduces a new asymptotic analysis of fundamental solutions for elliptic equations with discontinuous coefficients, advancing understanding of their behavior near discontinuities.

Findings

Asymptotic formula for fundamental solutions near discontinuities

Application insights for inverse problems involving elliptic operators

Enhanced understanding of solution behavior in piecewise-smooth coefficient scenarios

Abstract

Asymptotic formula is derived for the behavior of the fundamental solution of the second-order elliptic self-adjoint operator with a piecewise-smooth coefficient in front of the senior derivatives near the discontinuity surface of the coefficient. Applications to inverse problems are discussed.