Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary

Published: Nov 20, 2018
Abstract
Our topological setting is a smooth compact manifold of dimension two or higher with smooth boundary. Although this underlying topological structure is smooth, the Riemannian metric tensor is only assumed to be bounded and measurable. This is known as a rough Riemannian manifold. For a large class of boundary conditions we demonstrate a Weyl law for the asymptotics of the eigenvalues of the Laplacian associated to a rough metric. Moreover, we...
Paper Details
Title
Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary
Published Date
Nov 20, 2018
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