Concepedia

Various Properties of Solutions of the Infinity-Laplacian Equation

Lawrence C. Evans, Yifeng Yu

Communications in Partial Differential Equations · 2005 · 40 citations · 9 references

DOI

Concepts

Abstract

ABSTRACT We collect a number of technical assertions and related counterexamples about viscosity solutions of the infinity-Laplacian PDE − Δ∞ u = 0 for .

References

9

Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient

Robert Jensen · Archive for Rational Mechanics and Analysis · 1993 · 444 citations

, , +10

Optimal Lipschitz extensions and the infinity laplacian

Michael G. Crandall, L. C. Evans, Ronald Gariepy · Calculus of Variations and Partial Differential Equations · 2001 · 226 citations

, , +9

On the partial differential equation u ${}_{x}^{2}$ uxx+2uxuyuxy+u ${}_{y}^{2}$ uyy=0

Gunnar Aronsson · Arkiv för matematik · 1968 · 147 citations · Full text

, , +8

C1 Regularity for Infinity Harmonic Functions in Two Dimensions

Ovidiu Savin · Archive for Rational Mechanics and Analysis · 2005 · 136 citations

, , +8

A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions

Adam M. Oberman · Mathematics of Computation · 2004 · 107 citations · Full text

, , +16