Advances in Differential Equations

Sobolev regularity for solutions of parabolic equations by extrapolation methods

Gabriella Di Blasio

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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.

Article information

Adv. Differential Equations, Volume 6, Number 4 (2001), 481-512.

First available in Project Euclid: 2 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34G10: Linear equations [See also 47D06, 47D09]
Secondary: 35A22: Transform methods (e.g. integral transforms) 35B65: Smoothness and regularity of solutions 35K90: Abstract parabolic equations 46M35: Abstract interpolation of topological vector spaces [See also 46B70] 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]


Di Blasio, Gabriella. Sobolev regularity for solutions of parabolic equations by extrapolation methods. Adv. Differential Equations 6 (2001), no. 4, 481--512.

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