Superposition principle on the viscosity solutions of infinity Laplace equations

DOI10.1016/j.na.2018.01.011zbMath1392.35111OpenAlexW2794177453MaRDI QIDQ1744655

Xiaomeng Feng, Guanghao Hong

Publication date: 19 April 2018

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

Full work available at URL: https://doi.org/10.1016/j.na.2018.01.011

zbMATH Keywords

viscosity solutionsinfinity Laplace equation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Degenerate elliptic equations (35J70) Regularity of solutions in optimal control (49N60)

Related Items (4)

Viscosity solutions to inhomogeneous Aronsson's equations involving Hamiltonians \(\langle A(x)p,p\rangle \) ⋮ On the \(\infty \)-Laplacian on Carnot groups ⋮ Pointwise boundary differentiability for the infinity Laplace equations ⋮ Slope estimate and boundary differentiability for inhomogeneous infinity Laplace equation on convex domains

Cites Work

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• \(C^1\) regularity for infinity harmonic functions in two dimensions
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• Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
• \(C^{1,\alpha}\) regularity for infinity harmonic functions in two dimensions
• Slope estimate and boundary differentiability for inhomogeneous infinity Laplace equation on convex domains
• \(C^1\)-boundary regularity of planar infinity harmonic functions
• Counterexample to \(C^1\) boundary regularity of infinity harmonic functions
• Inhomogeneous infinity Laplace equation
• Extension of functions satisfying Lipschitz conditions
• Boundary differentiability of infinity harmonic functions
• Notes on the Infinity Laplace Equation
• On the regularity of solutions of the inhomogeneous infinity Laplace equation
• Optimal Lipschitz extensions and the infinity Laplacian

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