Calculus of Variations and Geometric Measure Theory

M. Bardi - A. Cesaroni

Liouville properties and critical value of fully nonlinear elliptic operators

created by cesaroni on 13 Apr 2016
modified on 23 Aug 2016


Published Paper

Inserted: 13 apr 2016
Last Updated: 23 aug 2016

Journal: J. Differential Equations
Volume: 261
Number: 7
Pages: 2701-2729
Year: 2016


We prove some Liouville properties for sub- and supersolutions of fully nonlinear degenerate elliptic equations in the whole space. Our assumptions allow the coefficients of the first order terms to be large at infinity, provided they have an appropriate sign, as in Ornstein- Uhlenbeck operators. We give two applications. The first is a stabilization property for large times of solutions to fully nonlinear parabolic equations. The second is the solvability of an ergodic Hamilton-Jacobi-Bellman equation that identifies a unique critical value of the operator.