TheNeumann Laplacian on spaces of continuous functions


If \Omega \subset \mathbb{R}^N is an open set, one can always define the Laplacian with Neumann boundary conditions \Delta^N_\Omega on L^2(\Omega). It is a self-adjoint operator generating a C_O-semigroup on L^2(\Omega). Considering the part \Delta^N_\Omega,c of \Delta^N_\Omega in C(\overline{\Omega}),we ask under which conditions on it generates a C_O-semigroup.

DOI Code: 10.1285/i15900932v22n1p65

Keywords: Neumann Laplace

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