M. Van Den Berg et P. Gilkey, Heat content asymptotics with inhomogeneous Neumann and Dirichlet boundaryconditions, POTENT ANAL, 14(3), 2001, pp. 269-274
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.