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arXiv · 2409.11124

Comparison principle for general nonlocal Hamilton-Jacobi equations with superlinear gradient

Adina Ciomaga·Tri Minh Le·Olivier Ley·Erwin Topp
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Abstract

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 L\'evy 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, L\'evy-It\^o operators).

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Adina Ciomaga, Tri Minh Le, Olivier Ley, Erwin Topp. 2024-09-17. Comparison principle for general nonlocal Hamilton-Jacobi equations with superlinear gradient. https://arxiv.org/abs/2409.11124

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