Maximal regular boundary value problems in Banach-valued function spaces and applications
The paper is devoted to the investigation of nonlocal boundary value problems for differential operator equations of second order in Banach-valued function spaces. It is assumed that the principal parts of the differential operators generated by these problems are non-selfadjoint. The author considers nonhomogeneous boundary value problems for ordinary differential operator equations, partial differential operator equations with dependent coefficients in the principal part, and nonlocal initial boundary value problems for parabolic differential operator equations. He gives conditions for the maximal regularity, positivity and the Fredholmness of the problems in Banach-valued \(L_p\)-spaces. The results are applied to nonlocal boundary value problems for quasi-elliptic partial differential equations, to infinite systems of nonlocal boundary value problems for elliptic equations with variable coefficients, and to nonlocal initial boundary value problems for parabolic equations on cylindrical domains.
scientific article; zbMATH DE number 5164020
scientific article