Hadamard and Liouville Type Results for Fully Nonlinear Partial Differential Inequalities

DOI10.1142/S0219199703001014zbMath1040.35024MaRDI QIDQ4454540

Alessandra Cutrì, Italo Capuzzo-Dolcetta

Publication date: 8 March 2004

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

viscosity solutionelliptic equation

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) General theory of partial differential operators (47F05)

Related Items (21)

On the Liouville property for fully nonlinear equations with superlinear first-order terms ⋮ Liouville properties and critical value of fully nonlinear elliptic operators ⋮ Classification of supersolutions and Liouville theorems for some nonlinear elliptic problems ⋮ Liouville results for fully nonlinear equations modeled on Hörmander vector fields. I: The Heisenberg group ⋮ Liouville theorems for fully nonlinear elliptic equations on spherically symmetric Riemannian manifolds ⋮ A note on the nonexistence of positive supersolutions to elliptic equations with gradient terms ⋮ Liouville results for fully nonlinear integral elliptic equations in exterior domains ⋮ Fully nonlinear degenerate operators associated with the Heisenberg group: barrier functions and qualitative properties ⋮ Nonexistence of positive supersolutions to some nonlinear elliptic problems ⋮ Positive supersolutions of non-autonomous quasilinear elliptic equations with mixed reaction ⋮ Fundamental solutions and Liouville type theorems for nonlinear integral operators ⋮ Liouville theorem for the fractional Lane-Emden equation in an unbounded domain ⋮ Some new Liouville-type results for fully nonlinear PDEs on the Heisenberg group ⋮ On Liouville type theorems for fully nonlinear elliptic equations with gradient term ⋮ Liouville type theorems for elliptic equations with gradient terms ⋮ Nonexistence of nonconstant solutions of some degenerate Bellman equations and applications to stochastic control ⋮ Harnack inequalities and ABP estimates for nonlinear second-order elliptic equations in unbounded domains ⋮ The Alexandrov-Bakelman-Pucci Weak Maximum Principle for Fully Nonlinear Equations in Unbounded Domains ⋮ Explicit subsolutions and a Liouville theorem for fully nonlinear uniformly elliptic inequalities in halfspaces ⋮ Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle ⋮ Liouville type results for periodic and almost periodic linear operators

Cites Work

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• Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
• On the Liouville property for fully nonlinear equations
• Existence and nonexistence of solutions of nonlinear Dirichlet problems with first order terms
• On the strong maximum principle for fully nonlinear degenerate elliptic equations
• Operatori ellittice estremanti
• User’s guide to viscosity solutions of second order partial differential equations
• Liouville theorems for elliptic inequalities and applications
• Teoremi di Liouville e stime a priori per equazioni ellittiche semilineari

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