Propagation of maxima and strong maximum principle for viscosity solutions of degenerate elliptic equations. I: Convex operators

DOI10.1016/S0362-546X(99)00317-XzbMath1135.35342MaRDI QIDQ5940172

Francesca Da Lio, Martino Bardi

Publication date: 9 June 2002

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

zbMATH Keywords

maximum principleviscosity solutiondegenerate elliptic equation

Mathematics Subject Classification ID

Related Items (15)

Large Critical Exponents for Some Second Order Uniformly Elliptic Operators ⋮ Strong maximum principle and boundary estimates for nonhomogeneous elliptic equations ⋮ On a strong maximum principle for fully nonlinear subelliptic equations with Hörmander condition ⋮ Nonexistence of nonconstant solutions of some degenerate Bellman equations and applications to stochastic control ⋮ Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle ⋮ The ergodic problem for some subelliptic operators with unbounded coefficients ⋮ A short proof of the \(C^{0,\alpha }\)-regularity of viscosity subsolutions for superquadratic viscous Hamilton-Jacobi equations and applications ⋮ Nonlinear eigenvalues and bifurcation problems for Pucci's operators ⋮ Maximum principle and propagation for intrinsicly regular solutions of differential inequalities structured on vector fields ⋮ Almost sure properties of controlled diffusions and worst case properties of deterministic systems ⋮ Ergodic mean field games with Hörmander diffusions ⋮ A note on the strong maximum principle for fully nonlinear equations on Riemannian manifolds ⋮ Regularity properties for a class of non-uniformly elliptic Isaacs operators ⋮ Directional ellipticity on special domains: weak maximum and Phragmén-Lindelöf principles ⋮ New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs

Cites Work

• Comparison principles and pointwise estimates for viscosity solutions of nonlinear elliptic equations
• Lectures on topics in stochastic differential equations
• Strong maximum principle for semicontinuous viscosity solutions of nonlinear partial differential equations
• Viscosity solutions and applications. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME), Montecatini Terme, Italy, June 12-20, 1995
• On the strong maximum principle for fully nonlinear degenerate elliptic equations
• Hypoelliptic second order differential equations
• Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
• Optimal control of diffustion processes and hamilton-jacobi-bellman equations part I: the dynamic programming principle and application
• User’s guide to viscosity solutions of second order partial differential equations
• On degenerate elliptic-parabolic operators of second order and their associated diffusions
• Variational Analysis
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
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