Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms

Shigeaki Koike (1) , Olivier Ley (2)

1 Mathematical Institute
2 IRMAR - Institut de Recherche Mathématique de Rennes

We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to $Du$. We prove several comparison principles among viscosity solutions which may be unbounded under some polynomial-type growth conditions. Our main result applies to PDEs with convex superlinear terms but we also obtain some results in nonconvex cases. Applications to monotone systems of PDEs are given.

Mots clés: viscosity solution; comparison principle; linearization

Domaines: Equations aux dérivées partielles [math.AP]

Shigeaki Koike, Olivier Ley. Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms. Journal of Mathematical Analysis and Applications, 2011, 381 (1), pp.110-120. ⟨10.1016/j.jmaa.2011.03.009⟩. ⟨hal-00522569⟩