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September  2004, 3(3): 395-415. doi: 10.3934/cpaa.2004.3.395

Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations

Francesca Da Lio 1,

1. 

Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino, Italy

Received  September 2003 Revised  March 2004 Published  June 2004

We prove a Strong Maximum Principle for upper semicontinuous viscosity subsolutions to fully nonlinear degenerate parabolic pde's. We also describe the set of propagation of maxima in the case of second order Hamilton-Jacobi-Bellman equations which are either convex or concave with respect to the $(u,Du,D^2 u)$ variables and we derive the Strong Maximum Principle in some cases, including a class of nonlinear operators which are not strictly parabolic.
Keywords: Hamilton-Jacobi equations, fully nonlinear pde's, Strong maximum principle, viscosity solutions., propagation of maxima, degenerate parabolic equations.
Mathematics Subject Classification: 35B50, 35J60, 35K65, 70H20, 49L2.
Citation: Francesca Da Lio. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Communications on Pure and Applied Analysis, 2004, 3 (3) : 395-415. doi: 10.3934/cpaa.2004.3.395
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