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Zbl 1129.35369
Birindelli, Isabeau; Demengel, Françoise
Comparison principle and Liouville type results for singular fully nonlinear operators. (English)
[J] Ann. Fac. Sci. Toulouse, Math. (6) 13, No. 2, 261-287 (2004). ISSN 0240-2963

Summary: We consider a large class of degenerate or singular operators $F$ defined on $\bbfR\times(\bbfR^N)^*\times S$, where $S$ denotes the space of symmetric matrices on $\bbfR^n$, $F$ is continuous. We give a new definition of viscosity sub and super solutions for $ F(x,\nabla u,\nabla^2 u)=0$. We prove a comparison theorem between sup and supersolutions for $ F(x,\nabla u,\nabla^2 u)=b(u) $ where $b$ is an increasing function, and a Liouville type result.

MSC 2000:: *35J60 Nonlinear elliptic equations
35B05 General behavior of solutions of PDE
35B50 Maximum principles (PDE)

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