A Hölder infinity Laplacian
CMAP, École Polytechnique, 91128
2 Dept. of Mathematical Sciences, NTNU, 7491 Trondheim, Norway
3 Université Paris-Est, Cermics, École des Ponts ParisTech, 6-8, avenue Blaise-Pascal, 77455 Marne-la-Vallée Cedex 2, France
In this paper we study the limit as p → ∞ of minimizers of the fractional Ws,p-norms. In particular, we prove that the limit satisfies a non-local and non-linear equation. We also prove the existence and uniqueness of solutions of the equation. Furthermore, we prove the existence of solutions in general for the corresponding inhomogeneous equation. By making strong use of the barriers in this construction, we obtain some regularity results.
Mathematics Subject Classification: 35D40 / 35J60 / 35J65
Key words: Lipschitz extensions / Hölder extensions / infinity Laplacian / non-local and non-linear equations / viscosity solutions
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