# American Institute of Mathematical Sciences

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

 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.
Citation: Francesca Da Lio. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Communications on Pure & Applied Analysis, 2004, 3 (3) : 395-415. doi: 10.3934/cpaa.2004.3.395
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