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Elliptic problems with boundary operators of higher orders in H\"ormander-Roitberg spaces. (arXiv:1802.00333v1 [math.AP])
来源于:arXiv
We investigate elliptic boundary-value problems for which the maximum of the
orders of the boundary operators is equal to or greater than the order of the
elliptic differential equation. We prove that the operator corresponding to an
arbitrary problem of this kind is bounded and Fredholm between appropriate
Hilbert spaces which form certain two-sided scales and are built on the base of
isotropic H\"ormander spaces. The differentiation order for these spaces is
given by an arbitrary real number and positive function which varies slowly at
infinity in the sense of Karamata. We establish a local a priori estimate for
the generalized solutions to the problem and investigate their local regularity
(up to the boundary) on these scales. As an application, we find sufficient
conditions under which the solutions have continuous classical derivatives of a
given order. 查看全文>>