Advances in Differential Equations

On the strong maximum principle for second order nonlinear parabolic integro-differential equations

Adina Ciomaga

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Abstract

This paper is concerned with the study of the Strong Maximum Principle for semicontinuous viscosity solutions of fully nonlinear, second-order parabolic integro-differential equations. We study separately the propagation of maxima in the horizontal component of the domain and the local vertical propagation in simply connected sets of the domain. We give two types of results for horizontal propagation of maxima: one is the natural extension of the classical results of local propagation of maxima and the other comes from the structure of the nonlocal operator. As an application, we use the Strong Maximum Principle to prove a Strong Comparison Result of viscosity sub- and supersolution for integro-differential equations.

Article information

Source
Adv. Differential Equations Volume 17, Number 7/8 (2012), 635-671.

Dates
First available in Project Euclid: 17 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355702971

Mathematical Reviews number (MathSciNet)
MR2963799

Zentralblatt MATH identifier
1264.35262

Subjects
Primary: 35R09: Integro-partial differential equations [See also 45Kxx] 35K55: Nonlinear parabolic equations 35B50: Maximum principles 35D40: Viscosity solutions

Citation

Ciomaga, Adina. On the strong maximum principle for second order nonlinear parabolic integro-differential equations. Adv. Differential Equations 17 (2012), no. 7/8, 635--671. https://projecteuclid.org/euclid.ade/1355702971.


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