Elliptic boundary-value problems in the sense of Lawruk on Sobolev and Hörmander spaces
英文摘要：
We investigate elliptic boundary-value problems with additional unknown functions in boundary conditions. These problems were introduced by Lawruk. We prove that the operator corresponding to such a problem is bounded and Fredholm on appropriate couples of the inner product isotropic Hörmander spaces $H^{s,φ}$, which form the refined Sobolev scale. The order of differentiation for these spaces is given by the real number $s$ and positive function $φ$ that varies slowly at infinity in the sense of Karamata. We consider this problem for an arbitrary elliptic equation $Au=f$ on a bounded Euclidean domain $Ω$ under the condition that $u\in H^{s,φ}(Ω)$, $s<\mathrm{ord}\,A$, and $f\in L_{2}(Ω)$. We prove theorems on the a priori estimate and regularity of the generalized solutions to this problem.
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