Comparison principles and Lipschitz regularity for some nonlinear degenerate elliptic equations

2016/12/30 by YanYan Li, Luc Nguyen, Bo Wang · 3 citations
Mathematics · #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP #math.DG

paper · pdf · doi:10.1007/s00526-018-1369-z

arxiv created 2016/12/30 · arxiv updated 2019/07/25

Abstract

We establish interior Lipschitz regularity for continuous viscosity solutions of fully nonlinear, conformally invariant, degenerate elliptic equations. As a by-product of our method, we also prove a weak form of the strong comparison principle, which we refer to as the principle of propagation of touching points, for operators of the form ∇² ψ+ L(x,ψ,∇ ψ) which are non-decreasing in ψ.

Citations

• Asymptotic behavior of solutions to the σ k -Yamabe equation near isolated singularities
• The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian
• Conformal geometry, contact geometry, and the calculus of variations

Cited by

• On the Neumann problem for the degenerate mixed equations arising in conformal geometry
• The fully nonlinear Loewner-Nirenberg problem: Liouville theorems and counterexamples to local boundary estimates
• The σ_k-Loewner-Nirenberg problem on Riemannian manifolds for k=(n)/(2) and beyond

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• Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry