Regularity of viscosity solutions of the σ_k-Yamabe-type Problem for k>n/2

2024/07/11 by Jinyang Wu, Wu, Jinyang · 1 citation
Mathematics · #Nonlinear Partial Differential Equations #Navier-Stokes equation solutions #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2407.08300

Abstract

We study the regularity of Lipschitz viscosity solutions to the σ_k Yamabe problem in the negative cone case. If either k=n or the manifold is conformally flat and k>n/2, we prove that all Lipschitz viscosity solutions are smooth away from a closed set of measure zero. For the general k>n/2 case, under certain assumptions, we prove the existence of a Lipschitz viscosity solution that is smooth away from a closed set of measure zero.

Citations

• The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian

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• Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds

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