Comparison principles for nonlocal Hamilton-Jacobi equations

Gonzalo Dávila

doi:10.3934/dcds.2022061

Article Contents

2022, Volume 42, Issue 9: 4471-4488. Doi: 10.3934/dcds.2022061

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Comparison principles for nonlocal Hamilton-Jacobi equations

Gonzalo Dávila^,

Universidad Técnica Federico Santa María, Departamento de Matemática, Chile

^*Corresponding author: Gonzalo Dávila
^*Corresponding author: Gonzalo Dávila

Received: March 2022

Revised: April 2022

Early access: April 2022

Published: September 2022

The first author is supported by Fondecyt grant 1190209

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Abstract

We prove the comparison principle for viscosity sub and super solutions of degenerate nonlocal operators with general nonlocal gradient nonlinearities. The proofs apply to purely Hamilton-Jacobi equations of order $ 0<s<1 $.

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Mathematics Subject Classification: Primary: 35B51, 35D40; Secondary: 35R11.

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References

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