A Hölder infinity Laplacian

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 18, Issue 3, 2012, Pages 799-835

  Chambolle, Antonin ^a   Lindgren, Erik ^b   Monneau, Régis ^c  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^c UNIVERSITÉ PARIS EST   (France)

Author keywords

H lder extensions; Infinity Laplacian; Lipschitz extensions; Non local and non linear equations; Viscosity solutions

Indexed keywords

LAPLACE TRANSFORMS;

EXISTENCE AND UNIQUENESS OF SOLUTION; EXISTENCE OF SOLUTIONS; INFINITY LAPLACIAN; LIPSCHITZ EXTENSIONS; NONLOCAL; VISCOSITY SOLUTIONS;

LINEAR EQUATIONS;

EID: 84871530215     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv/2011182     Document Type: Article

References (17)

1. G. Aronsson, Extension of functions satisfying Lipschitz conditions. Ark. Mat. 6 (1967) 551-561.
2. G. Aronsson, On certain singular solutions of the partial differential equation u2xuxx + 2uxuyuxy + u2yuyy = 0. Manuscr. Math. 47 (1984) 133-151.
3. G. Aronsson, M.G. Crandall and P. Juutinen, A tour of the theory of absolutely minimizing functions. Bull. Am. Math. Soc. (N.S.) 41 (2004) 439-505.
4. G. Barles, E. Chasseigne and C. Imbert, On the Dirichlet problem for second-order elliptic integro-differential equations. Indiana Univ. Math. J. 57 (2008) 213-246.
5. T. Bhattacharya, E. Di Benedetto and J. Manfredi, Limits as p → ∞ of Δ pup = f and related extremal problems. Rend. Sem. Mat. Univ. Politec. Torino (1989), No. Special Issue (1991) 15-68, Some topics in nonlinear PDEs, Turin (1989).
6. C. Bjorland, L. Caffarelli and A. Figalli, Non-Local Tug-of-War and the Infinity Fractional Laplacian. Comm. Pure Appl. Math. (2011).
7. L.A. Caffarelli and A. Córdoba, An elementary regularity theory of minimal surfaces. Differential Integral Equations 6 (1993) 1-13.
8. V. Caselles, J.-M. Morel and C. Sbert, An axiomatic approach to image interpolation. IEEE Trans. Image Process. 7 (1998) 376-386.
9. M.G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27 (1992) 1-67.
10. E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces. preprint arXiv:1104.4345 (2011)
11. H. Lebesgue, Sur le problème de Dirichlet. Rend. Circ. Mat. Palermo 24 (1907) 371-402.
12. G. Lu and P. Wang, Inhomogeneous infinity Laplace equation. Adv. Math. 217 (2008) 1838-1868.
13. E.J. McShane, Extension of range of functions. Bull. Am. Math. Soc. 40 (1934) 837-842.
14. F. Memoli, J.-M. Sapiro and P. Thompson, Brain and surface warping via minimizing lipschitz extensions. IMA Preprint Series 2092 (2006).
15. K. Murota, Discrete convex analysis. SIAM Monographs on Discrete Mathematics and Applications, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2003).
16. A.M. Oberman, An explicit solution of the Lipschitz extension problem. Proc. Am. Math. Soc. 136 (2008) 4329-4338.
17. H. Whitney, Analytic extensions of differentiable functions defined in closed sets. Trans. Am. Math. Soc. 36 (1934) 63-89.