Singular solutions of Hessian fully nonlinear elliptic equations - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Advances and Applications in Discrete Mathematics Année : 2011

Singular solutions of Hessian fully nonlinear elliptic equations

Résumé

We study Hessian fully nonlinear uniformly elliptic equations and show that the second derivatives of viscosity solutions of those equations (in 12 or more dimensions) can blow up in an interior point of the domain. We prove that the optimal interior regularity of such solutions is no more than C^{1+\epsilon}, showing the optimality of the known interior regularity result. The same is proven for Isaacs equations. We prove the existence of non-smooth solutions to fully nonlinear Hessian uniformly elliptic equations in 11 dimensions. We study also the possible singularity of solutions of Hessian equations defined in a neighborhood of a point and prove that a homogeneous order 0<\alpha<1 solution of a Hessian uniformly elliptic equation in a punctured ball should be radial.

Dates et versions

hal-01335001 , version 1 (21-06-2016)

Identifiants

Citer

Nikolai Nadirashvili, Serge Vlăduţ. Singular solutions of Hessian fully nonlinear elliptic equations. Advances and Applications in Discrete Mathematics, 2011, 228 (3), pp.1718--1741. ⟨10.1016/j.aim.2011.06.030⟩. ⟨hal-01335001⟩
118 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More