2001 Sobolev regularity for solutions of parabolic equations by extrapolation methods
Gabriella Di Blasio
Adv. Differential Equations 6(4): 481-512 (2001). DOI: 10.57262/ade/1357140609

Abstract

Let $A$ be the generator of an analytic semigroup on a Banach space $X$. We study the Sobolev regularity of the solutions $u$ of the problem $u'(t)=Au(t)+f(t)$, for almost every $t\in (0,T)$, $u(0)=u_0$. Using extrapolation theory we can investigate optimal conditions for the data $f$ and $u_0$ guaranteeing $u\in W^{\alpha,p}(0,T;X)$ and obtain new existence results for generalized as well as differentiable solutions for parabolic equations.

Citation

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Gabriella Di Blasio. "Sobolev regularity for solutions of parabolic equations by extrapolation methods." Adv. Differential Equations 6 (4) 481 - 512, 2001. https://doi.org/10.57262/ade/1357140609

Information

Published: 2001
First available in Project Euclid: 2 January 2013

zbMATH: 1020.34049
MathSciNet: MR1798495
Digital Object Identifier: 10.57262/ade/1357140609

Subjects:
Primary: 34G10
Secondary: 35A22 , 35B65 , 35K90 , 46M35 , 47D06

Rights: Copyright © 2001 Khayyam Publishing, Inc.

Vol.6 • No. 4 • 2001
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