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

Shakhmurov, Veli B.

doi:https://doi.org/10.1155/IJMMS/2006/92134

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 092134 | https://doi.org/10.1155/IJMMS/2006/92134

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

Veli B. Shakhmurov¹

Received27 Dec 2004

Accepted30 Sept 2005

Published02 Jul 2006

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.

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Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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