Singular Solutions of Hessian Fully Nonlinear Elliptic Equations

Details Singular Solutions of Hessian Fully Nonlinear Elliptic Equations Singular Solutions of Hessian Fully Nonlinear Elliptic Equations

2008-05-17

arxiv.org/abs/0805.2694v2

Adv. Math., 228 (2011), 1718-1741

Mathematics

Analysis of PDEs

27 pages, submitted, two sections added

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Singular Solutions of Hessian Fully Nonlinear Elliptic Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Singular Solutions of Hessian Fully Nonlinear Elliptic Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Singular Solutions of Hessian Fully Nonlinear Elliptic Equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-614705