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

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

2008-07-09

arxiv.org/abs/0807.1487v1

Journal of Functional Analysis, Volume 257, Issue 5, 2009, Pages 1429-1444

Mathematics

Analysis of PDEs

16 pages, no figures

Scientific paper

10.1016/j.jfa.2009.05.009

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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