Some properties of layer potentials and boundary integral operators for the wave equation

TL;DR

This paper derives new time-domain estimates for layer potentials and boundary integral operators related to the acoustic wave equation, improving upon previous Laplace transform-based estimates using evolution equation theory.

Contribution

It introduces novel time-domain estimates for wave equation layer potentials and boundary operators, advancing the analytical tools available for acoustic wave analysis.

Findings

New time-domain estimates for layer potentials

Improved bounds over Laplace transform methods

Enhanced understanding of wave boundary operators

Abstract

In this work we establish some new estimates for layer potentials of the acoustic wave equation in the time domain, and for their associated retarded integral operators. These estimates are proven using time-domain estimates based on theory of evolution equations and improve known estimates that use the Laplace transform.