Irregular boundary value problems for second order elliptic differential-operator equations in UMD Banach spaces

Angelo Favini, Yakov Yakubov

Research output: Contribution to journalArticlepeer-review

Abstract

We prove coerciveness with a defect and Fredholmness of nonlocal irregular boundary value problems for second order elliptic differential-operator equations in UMD Banach spaces. Then, we prove coerciveness with a defect in both the space variable and the spectral parameter of the problem with a linear parameter in the equation. The results do not imply maximal Lp-regularity in contrast to previously considered regular case. In fact, a counterexample shows that there is no maximal Lp-regularity in the irregular case. When studying Fredholmness, the boundary conditions may also contain unbounded operators in perturbation terms. Finally, application to nonlocal irregular boundary value problems for elliptic equations of the second order in cylindrical domains are presented. Equations and boundary conditions may contain differential-integral parts. The spaces of solvability are Sobolev type spaces Wp,q2,2.

Original languageEnglish
Pages (from-to)601-632
Number of pages32
JournalMathematische Annalen
Volume348
Issue number3
DOIs
StatePublished - 2010

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