Heat content asymptotics with inhomogeneous Neumann and Dirichlet boundaryconditions

Let M be a compact manifold with smooth boundary. We establish the existenc e of an asymptotic expansion for the heat content asymptotics of M with inh omogeneous Neumann and Dirichlet boundary conditions. We prove all the coef ficients are locally determined and determine the first several terms in th e asymptotic expansion.