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arXiv · 1902.07452

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

Anup Biswas·József Lőrinczi
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Abstract

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

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Anup Biswas, József Lőrinczi. 2019-02-20. Hopf's lemma for viscosity solutions to a class of non-local equations with applications. https://arxiv.org/abs/1902.07452

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