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An elliptic boundary problem acting on generalized Sobolev spaces. (arXiv:1710.01959v1 [math.AP])
来源于:arXiv
We consider an elliptic boundary problem over a bounded region $\Omega$ in
$\mathbb{R}^n$ and acting on the generalized Sobolev space
$W^{0,\chi}_p(\Omega)$ for $1 < p < \infty$. We note that similar problems for
$\Omega$ either a bounded region in $\mathbb{R}^n$ or a closed manifold acting
on $W^{0,\chi}_2(\Omega)$, called H\"{o}rmander space, have been the subject of
investigation by various authors. Then in this paper we will, under the
assumption of parameter-ellipticity, establish results pertaining to the
existence and uniqueness of solutions of the boundary problem. Furthermore,
under the further assumption that the boundary conditions are null, we will
establish results pertaining to the spectral properties of the Banach space
operator induced by the boundary problem, and in particular, to the angular and
asymptotic distribution of its eigenvalues. 查看全文>>