Coercive boundary value problems for regular degenerate equations

This study focuses on nonlocal boundary value problems (BVP) for degenerate elliptic differential-operator equations (DOE), that axe defined in Banach-valued function spaces, where boundary conditions contain a degenerate function and a principal part of the equation possess varying coefficients. Several conditions obtained, that, guarantee the maximal L-p regularity and fredholmness. At first a DOE with constant coefficients in the principal part, are investigated, where considered domain depends on certain parameter. In this case uniform maximal L-p-regularity and fredholmess with respect to the domain parameter are showed

Maximal B-regular boundary value problems with parameters

This study focuses on non-local boundary value problems (BVP) for elliptic differential-operator equations (DOE) defined in Banach-valued Besov (B) spaces. Here equations and boundary conditions contain certain parameters. This study found some conditions that guarantee the maximal regularity and fredholmness in Banach-valued B-spaces uniformly with respect to these parameters. These results are applied to non-local boundary value problems for a regular elliptic partial differential equation with parameters on a cylindrical domain to obtain algebraic conditions that guarantee the same properties. (c) 2005 Published by Elsevier Inc