The Asymptotics of The Laplacian on a Manifold with Boundary
Thomas Branson, Peter Gilkey · Communications in Partial Differential Equations · 1990
Let P be a second-order differential operator with leading symbol given by the tensor on a compact Riemannian manifold with boundary. We compute the asymptotics of the heat equation for Dirichlet, Neumann, and mixed boundary conditions.