Coercive boundary value problems for regular degenerate equations

Abstract

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.