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fractional laplacians

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Cauchy problem and periodic homogenization for nonlocal Hamilton–Jacobi equations with coercive gradient terms
Part of
Martino Bardi, Annalisa Cesaroni, Erwin Topp
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 6 / December 2020

Published online by Cambridge University Press:

17 September 2019, pp. 3028-3059

Print publication:

December 2020
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This paper deals with the periodic homogenization of nonlocal parabolic Hamilton–Jacobi equations with superlinear growth in the gradient terms. We show that the problem presents different features depending on the order of the nonlocal operator, giving rise to three different cell problems and effective operators. To prove the locally uniform convergence to the unique solution of the Cauchy problem for the effective equation we need a new comparison principle among viscosity semi-solutions of integrodifferential equations that can be of independent interest.