Separable Differential Operators with Parameters

Author

Martin Bohner, Missouri University of Science and TechnologyFollow
Veli B. Shakhmurov

Abstract

In this paper, we study boundary value problems for parameter-dependent elliptic differential-operator equations with variable coefficients in smooth domains. Uniform regularity properties and Fredholmness of this problem are obtained in vector-valued L_p-spaces. We prove that the corresponding differential operator is positive and is a generator of an analytic semigroup. Then, via maximal regularity properties of the linear problem, the existence and uniqueness of the solution to the nonlinear elliptic problem is obtained. As an application, we establish maximal regularity properties of the Cauchy problem for abstract parabolic equations, Wentzell-Robin-type mixed problems for parabolic equations, and anisotropic elliptic equations with small parameters.

Recommended Citation

M. Bohner and V. B. Shakhmurov, "Separable Differential Operators with Parameters," Differential Equations and Dynamical Systems, Springer Verlag, Jan 2020.

The definitive version is available at https://doi.org/10.1007/s12591-020-00542-8

Department(s)

Mathematics and Statistics

Keywords and Phrases

Banach-valued function spaces; Boundary value problems; Differential-operator equations; Interpolation of Banach spaces; Operator-valued multipliers; Semigroup of operators; Wentzell-Robin condition

International Standard Serial Number (ISSN)

0971-3514

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Springer Verlag, All rights reserved.

Publication Date

01 Jan 2020