We study the closed extensions (realizations) of differential operators subject to homogeneous boundary conditions on weighted L^p-Sobolev spaces over a manifold with boundary and conical singularities. Under natural ellipticity conditions we determine the domains of the minimal and the maximal extension. We show that both are Fredholm operators and give a formula for the relative index.
Realizations of differential operators on conic manifolds with boundary
CORIASCO, Sandro;SEILER, JOERG
2007-01-01
Abstract
We study the closed extensions (realizations) of differential operators subject to homogeneous boundary conditions on weighted L^p-Sobolev spaces over a manifold with boundary and conical singularities. Under natural ellipticity conditions we determine the domains of the minimal and the maximal extension. We show that both are Fredholm operators and give a formula for the relative index.
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