On the abstract Cauchy problem of parabolic type in spaces of continuous functions
type: Item
instance of: scholarly article
title: On the abstract Cauchy problem of parabolic type in spaces of continuous functions
zbMATH Open document ID: 0589.47042
DOI: 10.1016/0022-247X(85)90353-1
author: Eugenio Sinestrari
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: The main object of this paper is the study of the problem \[ u'(t)=Au(t)+f(t),\quad t\in [0,T];\quad u(0)=u_ 0 \] when f: [0,T]\(\to E\) (a Banach space), \(u_ 0\in E\) and A: D(A)\(\subseteq E\to E\) verifies all the properties of the generators of analytic semigroups with the possible exception of the density of D(A) in E. This gives the possibility of applying the abstract theory to Cauchy-Dirichlet problems for parabolic equations and obtain maximal regularity results in spaces of Hölder continuous functions.
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 46K15
zbMATH DE Number: 3946979
zbMATH Keywords: generators of analytic semigroups
zbMATH Keywords: abstract theory to Cauchy-Dirichlet problems for parabolic
zbMATH Keywords: equations
zbMATH Keywords: maximal regularity
zbMATH Keywords: spaces of Hölder continuous functions
zbMATH Keywords: abstract theory to Cauchy-Dirichlet problems for parabolic equations
MaRDI profile type: Publication
cites work: On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems
cites work: Existence and regularity for linear delay partial differential equations
cites work: Q5331410
cites work: Approximation theorems for semi-group operators in intermediate spaces
cites work: Q5549343
cites work: Q3931765
cites work: Sommes d'opérateurs linéaires et équations différentielles opérationnelles
cites work: Equations d'évolution abstraites non linéaires de type parabolique
cites work: Hölder regularity for non-autonomous abstract parabolic equations
cites work: Q5630031
cites work: Q5526485
cites work: Differential equation s in abstract spaces
cites work: Q5562267
cites work: Q3276084
cites work: Analyticity of the maximal solution of an abstract nonlinear parabolic equation
cites work: Interpolation Spaces Between Domains of Elliptic Operators and Spaces of Continuous Functions with Applications to Nonlinear Parabolic Equations
cites work: Q4100575
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Q4744844
cites work: Q3669959
cites work: Q3719122
cites work: Semi-linear evolution equations in interpolation spaces
cites work: Generation of Analytic Semigroups by Strongly Elliptic Operators
cites work: Generation of Analytic Semigroups by Strongly Elliptic Operators Under General Boundary Conditions
cites work: Q3207428
cites work: Q4169288
cites work: Q5664286
cites work: Q5620934
description: scientific article; zbMATH DE number 3946979