Advances in Differential Equations

Elliptic equations in non-smooth plane domains with an application to a parabolic problem

Fabrizio Colombo, Davide Guidetti, and Alfredo Lorenzi

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In this paper we study elliptic boundary-value problems in bounded non-smooth plane domains and prove a generation result concerning analytic semigroups of linear bounded operators in space of continuous functions. Then we apply such a generation result for bounded non-smooth plane domains to a parabolic integro-differential equation.

Article information

Adv. Differential Equations, Volume 7, Number 6 (2002), 695-716.

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J25: Boundary value problems for second-order elliptic equations
Secondary: 34G10: Linear equations [See also 47D06, 47D09] 35K10: Second-order parabolic equations 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]


Colombo, Fabrizio; Guidetti, Davide; Lorenzi, Alfredo. Elliptic equations in non-smooth plane domains with an application to a parabolic problem. Adv. Differential Equations 7 (2002), no. 6, 695--716.

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