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

Francesca Da Lio

doi:10.3934/cpaa.2004.3.395

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2004, Volume 3, Issue 3: 395-415. Doi: 10.3934/cpaa.2004.3.395

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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

Received: August 31, 2003

Revised: February 29, 2004

Published: August 2004

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Abstract

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.

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Mathematics Subject Classification: 35B50, 35J60, 35K65, 70H20, 49L25.

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