A note on the Liouville method applied to elliptic eventually degenerate fully nonlinear equations governed by the Pucci operators and the Keller-Osserman condition

DOI10.1007/S00208-011-0678-8zbMath1243.35033OpenAlexW2019298111MaRDI QIDQ422375

Gregorio Díaz

Publication date: 16 May 2012

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-011-0678-8

zbMATH Keywords

Keller-Osserman conditionPucci extremal operatorsstrong absorption term

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) A priori estimates in context of PDEs (35B45) Viscosity solutions to PDEs (35D40) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (12)

Some qualitative properties for geometric flows and its Euler implicit discretization ⋮ On the inequality \(F(x,D^2u)\geq f(u) +g(u)| Du|^q\) ⋮ Liouville property for solutions of the linearized degenerate thin film equation of fourth order in a halfspace ⋮ Generalized Keller-Osserman conditions for fully nonlinear degenerate elliptic equations ⋮ Harnack inequality for nonlinear elliptic equations with strong absorption ⋮ Large solutions of elliptic semilinear equations non-degenerate near the boundary ⋮ On some degenerate elliptic equations arising in geometric problems ⋮ Existence of positive entire solutions of fully nonlinear elliptic equations ⋮ On Liouville-type theorems for \(k\)-Hessian equations with gradient terms ⋮ A Few Recent Results on Fully Nonlinear PDE’s ⋮ Entire Solutions of a Nonlinear Diffusion System ⋮ Existence theorems for a class of systems involving two quasilinear operators

Cites Work

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• On solutions of δu=f(u)
• Superlinear elliptic equation for fully nonlinear operators without growth restrictions for the data
• An a priori interior estimate for the solutions of a non-linear problem representing weak diffusion
• User’s guide to viscosity solutions of second order partial differential equations
• Nonlinear elliptic equations in \(\mathbb{R}^N\) with ``absorbing zero order terms

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