Hopf's lemma for viscosity solutions to a class of non-local equations\n with applications

2019/02/20 by Anup Biswas, Biswas, Anup, József Lőrinczi +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1902.07452

openalex publication_date 2019/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a large family of integro-differential equations and establish a\nnon-local counterpart of Hopf's lemma, directly expressed in terms of the\nsymbol of the operator. As closely related problems, we also obtain a variety\nof maximum principles for viscosity solutions. In our approach we combine\ndirect analysis with functional integration, allowing a robust control around\nthe boundary of the domain, and make use of the related ascending ladder\nheight-processes. We then apply these results to a study of principal\neigenvalue problems, the radial symmetry of the positive solutions, and the\noverdetermined non-local torsion equation.\n

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