Nonlocal Liouville theorems with gradient nonlinearity

2024/07/23 by Biswas, Anup, Quaas, Alexander, Topp, Erwin · 7 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.16147

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.

Cited by

• Liouville--Type Results for Infinity Elliptic Equations Involving Gradient and Hardy--Hénon Nonlinearities
• Regularity theory for degenerate fully nonlinear nonlocal equations with a Hamiltonian term
• A unified clasification of Liouville properties and nontrivial solution for fractional elliptic equations with general Hénon-type superquadratic and gradient growth
• Liouville results for supersolutions of fractional p-Laplacian equations with gradient nonlinearities
• Liouville results for (p,q)-Laplacian elliptic equations with source terms involving gradient nonlinearities
• Classification of solutions of an elliptic Hamilton-Jacobi equation
• Improved Hölder regularity of fractional (p,q)-Poisson equation with regular data

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