Báo Cáo Báo cáo hóa học MAXIMAL REGULAR BOUNDARY VALUE PROBLEMS IN BANACH-VALUED WEIGHTED SPACE RAVI P AGARW

MAXIMAL REGULAR BOUNDARY VALUE PROBLEMS IN BANACH-VALUED WEIGHTED SPACE RAVI P. AGARWAL, MARTIN BOHNER, AND VELI B. SHAKHMUROV Received 10 July 2004 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 Banachvalued weighted L p 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. 1. Introduction and notation Boundary