Differential and Integral Equations

Higher order ordinary differential-operator equations on the whole axis in UMD Banach spaces

Angelo Favini and Yakov Yakubov

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Abstract

We use a direct approach for proving an isomorphism result for a general higher order abstract ordinary differential equation in a UMD Banach space. In fact, it gives maximal $L_p$-regularity property. As a consequence, we get some interpolation theorem (about intermediate derivatives). A situation of a higher order equation generated by one operator is also treated. Finally, we present some application to elliptic PDEs.

Article information

Source
Differential Integral Equations, Volume 21, Number 5-6 (2008), 497-512.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356038630

Mathematical Reviews number (MathSciNet)
MR2483266

Zentralblatt MATH identifier
1224.34186

Subjects
Primary: 34G10: Linear equations [See also 47D06, 47D09]
Secondary: 35J40: Boundary value problems for higher-order elliptic equations 47A56: Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones) 47N20: Applications to differential and integral equations

Citation

Favini, Angelo; Yakubov, Yakov. Higher order ordinary differential-operator equations on the whole axis in UMD Banach spaces. Differential Integral Equations 21 (2008), no. 5-6, 497--512. https://projecteuclid.org/euclid.die/1356038630


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