Advances in Differential Equations

Singular integro-differential equations of parabolic type

Angelo Favini, Alfredo Lorenzi, and Hiroki Tanabe

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We study a linear singular first-order integro-differential Cauchy problems in Banach spaces. Singular here means that the integro differential equation is not in normal form neither can it be reduced to such a form. We generalize to this context some existence and uniqueness theorems known for differential equations. Particular attention is given to single out the optimal regularity properties of solutions as well as to point out several explicit applications related to singular partial integro-differential of parabolic type.

Article information

Adv. Differential Equations, Volume 7, Number 7 (2002), 769-798.

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]
Secondary: 35K90: Abstract parabolic equations 35R10: Partial functional-differential equations 45J05: Integro-ordinary differential equations [See also 34K05, 34K30, 47G20] 49N20: Periodic optimization


Favini, Angelo; Lorenzi, Alfredo; Tanabe, Hiroki. Singular integro-differential equations of parabolic type. Adv. Differential Equations 7 (2002), no. 7, 769--798.

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