A HOLDER INFINITY LAPLACIAN

作者：Chambolle Antonin^*; Lindgren Erik; Monneau Regis

来源：ESAIM: Control, Optimisation and Calculus of Variations , 2012, 18(3): 799-835.

DOI：10.1051/cocv/2011182

• Lipschitz extensions
• Holder extensions
• infinity Laplacian
• non-local and non-linear equations
• viscosity solutions

In this paper we study the limit as p -%26gt; infinity of minimizers of the fractional W-s,W-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.

• 出版日期2012-7