Singular Solutions of Hessian Fully Nonlinear Elliptic Equations

@misc{citeulike:2895798, abstract = {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. 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.}, author = {Nadirashvili, Nikolai and Vladuts, Serge }, citeulike-article-id = {2895798}, eprint = {0805.2694}, keywords = {hessian, monge-ampere, regularity, viscosity-solution}, month = {May}, posted-at = {2008-06-15 09:00:54}, priority = {2}, title = {Singular Solutions of Hessian Fully Nonlinear Elliptic Equations}, url = {http://arxiv.org/abs/0805.2694}, year = {2008} }

TY - ELEC ID - citeulike:2895798 L3 - citeulike-article-id:2895798 TI - Singular Solutions of Hessian Fully Nonlinear Elliptic Equations N2 - 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. 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. KW - hessian KW - monge-ampere KW - regularity KW - viscosity-solution AU - Nadirashvili, Nikolai AU - Vladuts, Serge PY - 2008/May/17/ UR - http://arxiv.org/abs/0805.2694 ER -