Comparison Principle for Viscosity Solutions of Fully Nonlinear, Degenerate Elliptic Equations

DOI10.1080/03605300601113043zbMath1185.35084OpenAlexW1992327075MaRDI QIDQ5421517

Nickolai Kutev, Bernhard Kawohl

Publication date: 24 October 2007

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300601113043

zbMATH Keywords

viscosity solutioncomparison principledegenerate elliptic equationfully nonlinear elliptic equation

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Comparison principles in context of PDEs (35B51)

Related Items (15)

Hölder gradient regularity for the inhomogeneous normalized \(p(x)\)-Laplace equation ⋮ A Liouville-type theorem for fully nonlinear CR invariant equations on the Heisenberg group ⋮ Comparison principles and Lipschitz regularity for some nonlinear degenerate elliptic equations ⋮ Comparison principles for viscosity solutions of elliptic branches of fully nonlinear equations independent of the gradient ⋮ Robust maximization of asymptotic growth under covariance uncertainty ⋮ Symmetry of minimizers with a level surface parallel to the boundary ⋮ Numerical analysis of strongly nonlinear PDEs ⋮ Global regularity results for a class of singular/degenerate fully nonlinear elliptic equations ⋮ Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry ⋮ A note on the strong maximum principle for fully nonlinear equations on Riemannian manifolds ⋮ Strong comparison principles for some nonlinear degenerate elliptic equations ⋮ New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs ⋮ Remarks on the comparison principle for quasilinear PDE with no zeroth order terms ⋮ Statistical exponential formulas for homogeneous diffusion ⋮ Jump discontinuous viscosity solutions to second order degenerate elliptic equations

Cites Work

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• Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule
• Comparison principles and pointwise estimates for viscosity solutions of nonlinear elliptic equations
• Perron's method for Hamilton-Jacobi equations
• The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
• Strong maximum principle for semicontinuous viscosity solutions of nonlinear partial differential equations
• Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions
• On the strong maximum principle for fully nonlinear degenerate elliptic equations
• On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's
• User’s guide to viscosity solutions of second order partial differential equations
• Uniqueness and continuum of foliated solutions for a quasilinear elliptic equation with a non lipschitz nonlinearity
• The problem of dirichlet for quasilinear elliptic differential equations with many independent variables

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