Regular boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces |
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Authors: | Angelo Favini Veli Shakhmurov Yakov Yakubov |
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Affiliation: | (1) Dipartimento di Matematica, Universita di Bologna, piazza di Porta S. Donato, 5, Bologna, 40126, Italy;(2) Department of Mathematics Akfirat, Okan University, Tuzla, 34959, Istanbul, Turkey;(3) Raymond and Beverly Sackler School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, 69978, Israel |
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Abstract: | We consider coerciveness and Fredholmness of nonlocal boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces. In some special cases, the main coefficients of the boundary conditions may be bounded operators and not only complex numbers. Then, we prove an isomorphism, in particular, maximal L p -regularity, of the problem with a linear parameter in the equation. In both cases, the boundary conditions may also contain unbounded operators in perturbation terms. Finally, application to regular nonlocal boundary value problems for elliptic equations of the second order in non-smooth domains are presented. Equations and boundary conditions may contain differential-integral parts. The spaces of solvability are Sobolev type spaces W p,q 2,2. The first author is a member of G.N.A.M.P.A. and the paper fits the 60% research program of G.N.A.M.P.A.-I.N.D.A.M.; The third author was supported by the Israel Ministry of Absorption. |
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Keywords: | Abstract elliptic equation Elliptic boundary problem UMD Banach space R-sectorial operator Isomorphism Fredholmness |
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