Maximal regular boundary value problems in Banach-valued weighted space,” Boundary Value Problems

This study focuses on nonlocal boundary value problems for elliptic ordinary and par-tial 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 pa-rameter. Several conditions are obtained that guarantee the maximal regularity and Fred-holmness, estimates for the resolvent, and the completeness of the root elements of dif-ferential 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 differ-ential equations on cylindrical domain to obtain the algebraic conditions that guarantee the same properties