Regularity for fully nonlinear integro-differential operators with kernels of variable orders

2018/05/21 by Minhyun Kim, Kim, Minhyun, Ki-Ahm Lee +1
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1805.07955

openalex publication_date 2018/05/21 · openalex created_date 2018/06/01 · openalex updated_date 2026/08/01

Abstract

We consider fully nonlinear elliptic integro-differential operators with kernels of variable orders, which generalize the integro-differential operators of the fractional Laplacian type in \citeCS. Since the order of differentiability of the kernel is not characterized by a single number, we use the constant C_φ= ( ∫_ℝⁿ (1-cos y₁)/(\vert y \vertⁿ φ(\vert y \vert)) dy )^-1 instead of 2-σ, where φ satisfies a weak scaling condition. We obtain the uniform Harnack inequality and Hölder estimates of viscosity solutions to the nonlinear integro-differential equations.

Citations

• Hitchhikerʼs guide to the fractional Sobolev spaces

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