Optimal Lipschitz extensions and the infinity laplacian

被引：0
|
作者：
Crandall M.G. [1 ]
Evans L.C. [2 ]
Gariepy R.F. [3 ]
机构：
[1] Department of Mathematics, University of California, Santa Barbara
[2] Department of Mathematics, University of California, Berkeley
[3] Department of Mathematics, University of Kentucky, Lexington
来源：
Calculus of Variations and Partial Differential Equations | 2001年 / 13卷 / 2期
关键词：
Variational Principle; Boundary Data; Comparison Principle; Liouville Theorem; Lipschitz Extension;
D O I：
10.1007/s005260000065
中图分类号：
学科分类号：
摘要：
We reconsider in this paper boundary value problems for the so-called "infinity Laplacian" PDE and the relationships with optimal Lipschitz extensions of the boundary data. We provide some fairly elegant new proofs, which clarify and simplify previous work, and in particular draw attention to the fact that solutions may be characterized by a comparison principle with appropriate cones. We in particular show how comparison with cones directly implies the variational principle associated with the equation. In addition, we establish a Liouville theorem for subsolutions bounded above by planes.
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页码：123 / 139
页数：16
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