Separable Differential Operators with Parameters

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Date

2023

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Springer india

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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.

Description

Bohner, Martin/0000-0001-8310-0266

Keywords

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

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0

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Q2

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Volume

31

Issue

3

Start Page

581

End Page

611