This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter. Several conditions are obtained that guarantee the maximal regularity and Fredholmness, estimates for the resolvent, and the completeness of the root elements of differential operators generated by the corresponding boundary value problems in Banach-valued weighted Lp spaces. These results are applied to nonlocal boundary value problems for regular elliptic partial differential equations and systems of anisotropic partial differential equations on cylindrical domain to obtain the algebraic conditions that guarantee the same properties.
R. P. Agarwal et al., "Maximal Regular Boundary Value Problems in Banach-Valued Weighted Space," Boundary Value Problems, Hindawi Publishing, Jan 2005.
The definitive version is available at https://doi.org/10.1155/BVP.2005.9
Mathematics and Statistics
Keywords and Phrases
Banach-Valued Weighted Space; Fredholmness; Boundary Value; Elliptic Ordinary and Partial Differential-Operator Equations; Maximal Regularity
Article - Journal
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