Interior and boundary regularity of the wave equation with interior point control (Q1802866)

This paper considers interior and boundary regularity of wave equations on a bounded domain \(\Omega \subset \mathbb{R}^ n\), \(n=1,2,3\), subject to a point control (through a Dirac distribution \(\delta)\) at an interior point of \(\Omega\). These new interior regularity results are ``\({1\over 2}+\varepsilon\)'' sharper in space Sobolev regularity over those that can be obtained by simply using the regularity of \(\delta\). The boundary regularity results are ``\({1\over 2}\)'' sharper over those that can be inferred by applying trace theory to the interior results. Laplace- Fourier transform techniques are used.