Estimates for smooth absolutely minimizing Lipschitz extensions
Date
1993-10-12
Authors
Evans, Lawrence C.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
I present some elementary maximum principle arguments, establishing interior gradient bounds and Harnack inequalities for both u and |Du|, where u is a smooth solution of the degenerate elliptic PDE ∆∞u = 0. These calculations in particular extend to higher dimensions G. Aronsson’s assertion [2] that a nonconstant, smooth solution can have no interior critical point.
Description
Keywords
Lipschitz extensions, Harnack inequalities
Citation
Evans, L. C. (1993). Estimates for smooth absolutely minimizing Lipschitz extensions. <i>Electronic Journal of Differential Equations, 1993</i>(03), pp. 1-9.
Rights
Attribution 4.0 International