COMPARISON PRINCIPLE FOR GENERAL NONLOCAL HAMILTON-JACOBI EQUATIONS WITH SUPERLINEAR GRADIENT - Centre Henri Lebesgue
Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2024

COMPARISON PRINCIPLE FOR GENERAL NONLOCAL HAMILTON-JACOBI EQUATIONS WITH SUPERLINEAR GRADIENT

Résumé

We obtain the comparison principle for discontinuous viscosity sub-and supersolutions of nonlocal Hamilton-Jacobi equations, with superlinear and coercive gradient terms. The nonlocal terms are integro-differential operators in Lévy form, with general measures: x-dependent, possibly degenerate and without any restriction on the order. The measures must satisfy a combined Wasserstein/Total Variation-continuity assumption, which is one of the weakest conditions used in the context of viscosity approach for this type of integro-differential PDEs. The proof relies on a regularizing effect due to the gradient growth. We present several examples of applications to PDEs with different types of nonlocal operators (measures with density, operators of variable order, Lévy-Itô operators).

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Dates et versions

hal-04700567 , version 1 (17-09-2024)

Identifiants

  • HAL Id : hal-04700567 , version 1

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Adina Ciomaga, Minh Lê, Olivier Ley, Erwin Topp. COMPARISON PRINCIPLE FOR GENERAL NONLOCAL HAMILTON-JACOBI EQUATIONS WITH SUPERLINEAR GRADIENT. 2024. ⟨hal-04700567⟩
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