TheNeumann Laplacian on spaces of continuous functions
Abstract
If
is an open set, one can always define the Laplacian with Neumann boundary conditions
on
. It is a self-adjoint operator generating a
-semigroup on
. Considering the part
of
in
,we ask under which conditions on it generates a
-semigroup.
![\Omega \subset \mathbb{R}^N](http://212.189.136.205/plugins/generic/latexRender/cache/b7208ced3c5f454feb527133d6e099ee.png)
![\Delta^N_\Omega](http://212.189.136.205/plugins/generic/latexRender/cache/818d52b1b6c56a4ad7e378e439822533.png)
![L^2(\Omega)](http://212.189.136.205/plugins/generic/latexRender/cache/71f9aa3c12d35d276e58f2f44975f2bb.png)
![C_O](http://212.189.136.205/plugins/generic/latexRender/cache/74c4d5a9a8641a5a60582e3017c4a787.png)
![L^2(\Omega)](http://212.189.136.205/plugins/generic/latexRender/cache/71f9aa3c12d35d276e58f2f44975f2bb.png)
![\Delta^N_\Omega,c](http://212.189.136.205/plugins/generic/latexRender/cache/7bd81dad4e33cf7e55b9d2d3ddeb3299.png)
![\Delta^N_\Omega](http://212.189.136.205/plugins/generic/latexRender/cache/818d52b1b6c56a4ad7e378e439822533.png)
![C(\overline{\Omega})](http://212.189.136.205/plugins/generic/latexRender/cache/ab3016d53366444c957cbfa1a4def335.png)
![C_O](http://212.189.136.205/plugins/generic/latexRender/cache/74c4d5a9a8641a5a60582e3017c4a787.png)
DOI Code:
10.1285/i15900932v22n1p65
Keywords:
Neumann Laplace
Full Text: PDF