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November/December 2011 Abstract elliptic and parabolic systems with applications to problems in cylindrical domains
Angelo Favini, Davide Guidetti, Yakov Yakubov
Adv. Differential Equations 16(11/12): 1139-1196 (November/December 2011).

Abstract

We consider problems for quite general second-order abstract elliptic and corresponding parabolic equations on the interval $[0,1]$ and the rectangle $[0,T]\times [0,1]$, respectively. $R$-boundedness estimates of solutions of abstract boundary-value problems for elliptic equations with a parameter are established, in contrast to standard norm-bounded estimates. The results are applied to obtain $L^p$-maximal regularity for corresponding parabolic systems. In applications, the coefficient $A(x)$ of the solution $u$ can be $2m$-order elliptic operators with suitable boundary conditions, while the coefficient $B(x)$ of the first-order derivative of the solution $D_xu$ can be interpreted as an $m$-order differential operator. The corresponding applications to PDEs are presented.

Citation

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Angelo Favini. Davide Guidetti. Yakov Yakubov. "Abstract elliptic and parabolic systems with applications to problems in cylindrical domains." Adv. Differential Equations 16 (11/12) 1139 - 1196, November/December 2011.

Information

Published: November/December 2011
First available in Project Euclid: 17 December 2012

zbMATH: 1237.34110
MathSciNet: MR2858526

Subjects:
Primary: 34G10, 35J25, 35J40, 35K20, 35K35

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.16 • No. 11/12 • November/December 2011
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