On the strong maximum principle for second order nonlinear parabolic integro-differential equations
By Adina Ciomaga. Advances in Differential Equations, 2010
58 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/57b79cb159a8211f0e3c345a413caf39f7bef4fc
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In Applied Mathematics
- Serena Dipierro
- Enrico Valdinoci
- E. Vecchi
- Stefano Biagi
- Adina Ciomaga
- Emmanuel Chasseigne
- C. Imbert
- Guy Barles
In Control and Systems Engineering
- Serena Dipierro
- Enrico Valdinoci
- E. Vecchi
- Stefano Biagi
- Guy Barles
- Emmanuel Chasseigne
- C. Imbert
- Adina Ciomaga
Citations in the corpus
- Lipschitz regularity of solutions for mixed integro-differential equations (2011, background): “In a recent study of the strong maximum principle for integro-differential equation [8], the third author introduced another type of mixed ellipticity : at each point, the nonlinearity may be degenerate in the second-order term, and in the nonlocal term, but the combination of the local and the nonl”
- A Faber-Krahn inequality for mixed local and nonlocal operators (2021, background): “Operators of this type present interesting mathematical questions, especially due to the lack of scale invariance and in view of the combination of local and nonlocal behaviors; see [1, 3–5, 7, 8, 10, 14–18, 21–24, 29, 32, 35, 43, 44, 53].”