Differential and Integral Equations

Sturm-Liouville problems for an abstract differential equation of elliptic type in UMD spaces

Mustapha Cheggag, Angelo Favini, Rabah Labbas, Stéphane Maingot, and Ahmed Medeghri

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In this paper we give some new results on Sturm-Liouville abstract problems of second-order differential equations of elliptic type in UMD spaces. Existence, uniqueness and maximal regularity of the strict solution are proved using the celebrated Dore-Venni theorem. This work completes the problems studied by Favini, Labbas, Maingot, Tanabe and Yagi under Dirichlet boundary conditions, see [6].

Article information

Differential Integral Equations, Volume 21, Number 9-10 (2008), 981-1000.

First available in Project Euclid: 20 December 2012

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Zentralblatt MATH identifier

Primary: 35R20: Partial operator-differential equations (i.e., PDE on finite- dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]
Secondary: 34B05: Linear boundary value problems 34G10: Linear equations [See also 47D06, 47D09] 35J25: Boundary value problems for second-order elliptic equations 35J40: Boundary value problems for higher-order elliptic equations 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47N20: Applications to differential and integral equations


Cheggag, Mustapha; Favini, Angelo; Labbas, Rabah; Maingot, Stéphane; Medeghri, Ahmed. Sturm-Liouville problems for an abstract differential equation of elliptic type in UMD spaces. Differential Integral Equations 21 (2008), no. 9-10, 981--1000. https://projecteuclid.org/euclid.die/1356038596

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