Good and viscosity solutions of fully nonlinear elliptic equations

DOI10.1090/S0002-9939-01-06115-9zbMath0987.35055OpenAlexW1530854049MaRDI QIDQ2758991

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Publication date: 10 December 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-06115-9

zbMATH Keywords

fixed point methodapproximation procedure\(L^p\)-viscosity solutions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (6)

Large Critical Exponents for Some Second Order Uniformly Elliptic Operators ⋮ Strong-viscosity solutions: classical and path-dependent PDEs ⋮ Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations ⋮ Weak Uniqueness for Elliptic Operators in ℝ³ with Time-Independent Coefficients ⋮ Crandall-Lions viscosity solutions for path-dependent PDEs: the case of heat equation ⋮ On the Existence of Smooth Solutions for Fully Nonlinear Parabolic Equations with Measurable “Coefficients” without Convexity Assumptions

Cites Work

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• A remark on regularization in Hilbert spaces
• Uniformly elliptic PDEs with bounded, measurable coefficients
• \(W^{1,p}\)-interior estimates for solutions of fully nonlinear, uniformly elliptic equations
• Uniqueness in the Dirichlet problem for some elliptic operators with discontinuous coefficients
• On viscosity solutions of fully nonlinear equations with measurable ingredients

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