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Approximation of the Semigroup generated by the Robin Laplacian in terms of the Gaussian Semigroup · arXivDesk

0807.1487Jul 9, 200816 pages, no figures

Approximation of the Semigroup generated by the Robin Laplacian in terms of the Gaussian Semigroup

Robin Nittka

Abstract

For smooth bounded open sets in euclidean space, we construct corresponding contractive linear extension operators for the space of continuous functions which preserve regularity of functions in the domain of the Robin Laplacian. We also prove a Trotter-like approximation for the semigroup generated by the Laplacian subject to Robin boundary conditions in terms of these extension operators. The limiting case of Dirichlet boundary conditions is treated separately.

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The paper addresses: Approximation of the Semigroup generated by the Robin Laplacian in terms of the Gaussian Semigroup.
For smooth bounded open sets in euclidean space, we construct corresponding contractive linear extension operators for the space of continuous functions which preserve regularity of functions in the domain of the Robin Laplacian.