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arXiv · 2407.16147

Nonlocal Liouville theorems with gradient nonlinearity

Anup Biswas·Alexander Quaas·Erwin Topp
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Abstract

In this article we consider a large family of nonlinear nonlocal equations involving gradient nonlinearity and provide a unified approach, based on the Ishii-Lions type technique, to establish Liouville properties of the solutions. We also answer an open problem raised by [24]. Some applications to regularity issues are also studied.

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Anup Biswas, Alexander Quaas, Erwin Topp. 2024-07-23. Nonlocal Liouville theorems with gradient nonlinearity. https://arxiv.org/abs/2407.16147

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