A “maximum principle for semicontinuous functions” applicable to integro-partial differential equations

By Espen Robstad Jakobsen, Kenneth Hvistendahl Karlsen. 2006

151 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/22160ba31403b331e1dc0df5ca1473e6961d496b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Mixed local and nonlocal elliptic operators: regularity and maximum principles (2020, background): “The mathematical study of operators with different order is not new in itself, and indeed the literature already presents results concerning, among the others, the theory of viscosity solutions (see [37, 38, 6, 11, 21, 4, 5]), the Aubry-Mather theory for sums of different fractional Laplacians (see ”
Risk minimizing portfolios and HJBI equations for stochastic differential games (2008, unknown): “See [17].”
Existence and uniqueness of viscosity solutions for QVI associated with impulse control of jump-diffusions (2009, methodology): “For our proof of uniqueness, we will use and extend the framework as presented in the more recent paper [7] (the formulation in [23] does not permit an easy impulse control extension).”
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 [41, 42, 5, 22, 10, 18, 3, 17, 4, 53, 16, 23, 32, 24, 8, 7, 29, 15, 1, 14, 21, 45].”
Second-order elliptic integro-differential equations: viscosity solutions' theory revisited (2007, background): “A first attempt is made by Jakobsen and Karlsen [14] to give general results applicable to second-order elliptic equations.”
On the strong maximum principle for second order nonlinear parabolic integro-differential equations (2010, methodology): “Jakobsen and Karlsen in [20] used the original approach due to Jensen [21], Ishii [18], Ishii and Lions [17], Crandall and Ishii [13] and Crandall, Ishii and Lions [14] for proving comparison results for viscosity solutions of nonlinear degenerate elliptic integro-partial differential equations with”
Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion Processes (2010, background): “On the other hand, the viscosity solution approach to nonlocal equations is still under development and is currently an active research area, cf. for example [1, 2, 6, 7, 17, 29, 30, 31 , 38, 39].”
G-Lévy processes under sublinear expectations (2009, background): “We refer to [1, 4, 6, 7, 17, 24] and the references therein.”
CONTINUOUS DEPENDENCE ESTIMATES FOR VISCOSITY SOLUTIONS OF INTEGRO-PDES (2005, methodology): “The proof is similar to that in Sayah [45], see also [6, 35].”
RISK INDIFFERENCE PRICING IN JUMP DIFFUSION MARKETS (2009, methodology): “Sufficient conditions for the uniqueness of the viscosity solutions of the HJBI equation (5.5) are given in Jakobsen and Karlsen (2006) and Pham (1998).”
The Fisher-KPP problem with doubly nonlinear diffusion (2016, background): “The standard comparison principle for viscosity solutions also holds true (see [14, 15]).”
Nonlinear Lévy Processes and their Characteristics (2016, background): “The proof proceeds through the following general result, essentially due to [8] (which, in turn, draws from [2, 10]).”
On the Dirichlet Problem for Second-Order Elliptic Integro-Differential Equations (2008, methodology): “We refer the reader to Ishii [14] or the User’s guide [9] for the presentation of Perron’s method which extends to the case of non-local equations because of the general stability result for integro-differential equations of Bensaoud and Sayah [5] (see also [4]) and to [16,15,2,4] and references the”
A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models (2005, unknown): “This property can be extended to sub-solutions and super-solutions in the following sense [1, 19]: Proposition 3 (Comparison principle for semi-continuous solutions[1, 19]).”