Open AccessSymmetry results for viscosity solutions of fully nonlinear uniformly elliptic equations
Author(s) -
Francesca Da Lio,
Boyan Sirakov
Publication year - 2007
Publication title -
journal of the european mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.549
H-Index - 64
eISSN - 1435-9863
pISSN - 1435-9855
DOI - 10.4171/jems/81
Subject(s) - mathematics , symmetry (geometry) , nonlinear system , viscosity , mathematical analysis , elliptic curve , quarter period , viscosity solution , geometry , thermodynamics , physics , quantum mechanics
We study uniformly elliptic fully nonlinear equations $$ F(D^2u, Du, u, x)=0, $$ 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.
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