JournalsjemsVol. 9 , No. 2DOI 10.4171/jems/81

Symmetry results for viscosity solutions of fully nonlinear uniformly elliptic equations

  • Francesca Da Lio

    Università di Torino, Italy
  • Boyan Sirakov

    Ecole des hautes études en sciences sociales, Paris, France
Symmetry results for viscosity solutions of fully nonlinear uniformly elliptic equations cover

Abstract

We study uniformly elliptic fully nonlinear equations

F(D2u,Du,u,x)=0,F(D^2u, Du, u, x)=0,

and prove results of Gidas--Ni--Nirenberg type for positive viscosity solutions of such equations. We show that symmetries of the equation and the domain are reflected by the solution, both in bounded and unbounded domains.