Necessary and sufficient conditions for maximal regularity in the study of elliptic differential equations in Hölder spaces
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for maximal regularity in the study of elliptic differential equations in Hölder spaces
zbMATH Open document ID: 1165.34034
author: Angelo Favini
author: Rabah Labbas
author: Stéphane Maingot
author: Hiroki Tanabe
author: Atsushi Yagi
published in: Discrete and Continuous Dynamical Systems
publication date: 2008-10-30T00:00:00Z
review text: The authors obtain new and interesting results on complete abstract second order differential equations of elliptic type in the framework of Hölder spaces. The authors consider the second order abstract differential equation \[ u''(x) + 2 B u'(x) +Au(x) = f(x), \quad x \in (0, 1)\leqno(1) \] with the boundary conditions \[ u(0) = u_0 \quad u(1) = u_1\leqno(2) \] where \(X\) is a complex Banach space and \(A, B\) are two linear operators on \(X\), \(f\in C([0, 1]; X)\) and \(u_0, u_1 \in X\). When \(f\) is Hölder continuous and the operators \(A\) and \(B\) satisfy some natural assumptions, the authors give necessary and sufficient conditions of compatibility to obtain a strict solution \(u\) and also to ensure that the strict solution has the maximal regularity property.
reviewed by: Adina Luminiţa Sasu
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 5359503
zbMATH Keywords: second order abstract differential equations
zbMATH Keywords: boundary condition
zbMATH Keywords: analytic semigroup
zbMATH Keywords: maximal regularity
zbMATH Keywords: Hölderian regularity
MaRDI profile type: Publication
full work available at URL: dcds.2008.22.989
OpenAlex ID: W2000170852
DOI: 10.3934/DCDS.2008.22.989
description: scientific article; zbMATH DE number 5359503