International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 6, Pages 92134, 26 p.
doi:10.1155/IJMMS/2006/92134

Maximal regular boundary value problems in Banach-valued function spaces and applications

Abstract

The nonlocal boundary value problems for differential operator equations of second order with dependent coefficients are studied. The principal parts of the differential operators generated by these problems are non-selfadjoint. Several conditions for the maximal regularity and the Fredholmness in Banach-valued Lp-spaces of these problems are given. By using these results, the maximal regularity of parabolic nonlocal initial boundary value problems is shown. In applications, the nonlocal boundary value problems for quasi elliptic partial differential equations, nonlocal initial boundary value problems for parabolic equations, and their systems on cylindrical domain are studied.