Tsukuba Journal of Mathematics

Fractional powers and interpolation theory for multivalued linear operators and applications to degenerate differential equations

Alberto Favaron and Angelo Favini

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Abstract

We provide intermediate properties for the domains of the fractional powers of an abstract multivalued linear operator A of weak parabolic type. In particular, our results exhibit the special role played by the linear subspace A0, which reduces to {0} if and only if A is single-valued. The behaviour of the singular semigroup generated by A with respect to the domains of the fractional powers is then studied, and applications of this behaviour to questions of maximal time and space regularity for abstract multivalued evolution equations are given. As a concrete case we consider a class of degenerate partial differential evolution equations which may be rewritten in a multivalued evolution form.

Article information

Source
Tsukuba J. Math., Volume 35, Number 2 (2011), 259-323.

Dates
First available in Project Euclid: 13 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1331658708

Digital Object Identifier
doi:10.21099/tkbjm/1331658708

Mathematical Reviews number (MathSciNet)
MR2918321

Zentralblatt MATH identifier
1251.46009

Subjects
Primary: 46B70: Interpolation between normed linear spaces [See also 46M35] 47A06: Linear relations (multivalued linear operators) 47B99: None of the above, but in this section
Secondary: 35K65: Degenerate parabolic equations 44A45: Classical operational calculus 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]

Keywords
Fractional powers interpolation theory multivalued linear operators singular semigroups multivalued evolution equations degenerate differential equations

Citation

Favaron, Alberto; Favini, Angelo. Fractional powers and interpolation theory for multivalued linear operators and applications to degenerate differential equations. Tsukuba J. Math. 35 (2011), no. 2, 259--323. doi:10.21099/tkbjm/1331658708. https://projecteuclid.org/euclid.tkbjm/1331658708


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