The Wave Equation in Lp-Spaces

In the first part of the paper, Gaussian estimates are used to study $L^p$-summability of the solution of the wave equation in $L^p(Omega)$ associated with a general operator in divergence form with bounded coefficients. Secondly, we prove that if $Omega$ is a cube in $RR^N$, then the Laplacian with Dirichlet or Neumann boundary conditions generates an $al$-times integrated cosine function on $L^p(Omega),;1le p