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Session S18 - Recent progress in non-linear PDEs and their applications

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Improved Regularity for a Class of Nonlocal $\mathcal{L}_0$-Elliptic Equations with an Asymptotic Property

Aelson Sobral

Federal University of Paraíba(UFPB), Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We establish improved $\mathcal{C}^{1,(\sigma-1)^-}$ regularity estimates to viscosity solutions of a class of nonlocal $\mathcal{L}_0(\sigma)$-elliptic equations with an asymptotic property. We introduce the notion of recession operator to the nonlocal context, discuss the main features and compare with its classical version. The role of this class of equations is detailed on some examples and an improved regularity result.

Joint work with Disson dos Prazeres(Federal University of Sergipe(UFS), Brazil).

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