CONTINUOUS DEPENDENCE ESTIMATES FOR VISCOSITY SOLUTIONS OF INTEGRO-PDES

By Espen Robstad Jakobsen, Kenneth Hvistendahl Karlsen. 2005

135 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/5b9ac213e476fba285fd82500d85cb0f06b7f618

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Citations in the corpus

Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion Processes (2010, methodology): “The proof of the lemma is similar to the scalar case, see [30] or [38].”
Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations (2011, methodology): “[14] E. R. Jakobsen and K. H. Karlsen, Continuous dependence estimates for viscosity solutions of integro-PDEs, J. Differential Equations, 212 (2005), pp. 278–318.”
The Bernstein Technique for Integro-Differential Equations (2020, methodology): “In this respect, the closest work that we could find is [10], by Biswas, Jakobsen, andKarlsen, which concerns an integro-differential equation of parabolic type posed in thewhole space.”
A Hong-Krahn-Szegö inequality for mixed local and nonlocal operators (2021, background): “The study of mixed local/nonlocal operators has been recently received an increasing level of attention, both in view of their intriguing mathematical structure, which combines the classical setting and the features typical of nonlocal operators in a framework that is not scale-invariant [40, 45, 46”
Linear theory for a mixed operator with Neumann conditions (2020, unknown): “In terms of theory and applications, we recall that operators with mixed classical and fractional orders have been studied under different points of views, see for instance [1,2,4,6–10,12,13,18,19,21,25–27, 31–33,40,47,48] and the references therein.”
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].”
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 ”
Regularity results for solutions of mixed local and nonlocal elliptic equations (2022, background): “Moreover, mixed operators have recently received a great attention from different points of view, including regularity theory [2, 3, 8, 10, 12, 14, 15, 17, 25], existence and non-existence results [1, 6, 28], eigenvalue problems [13, 16, 22], shape optimization and calculus of variations [7, 11], sy”
A “maximum principle for semicontinuous functions” applicable to integro-partial differential equations (2006, result): “Although we only discuss elliptic integro-PDEs, it is not hard to formulate “parabolic” versions of our main results (for example Theorem 4.9), see [ 26 ].”