On convexity of level sets of p-harmonic functions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Zhang, Ting¹  Zhang, Wei² 

[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China

[2] Australian Natl Univ, Ctr Math & Its Applicat, Canberra, ACT 0200, Australia

关键词: Curvature estimates;    p-Harmonic functions;    Support function;    Maximum principle;   

DOI  :  10.1016/j.jde.2013.06.004

来源: Elsevier

【 摘 要 】

In this paper, we give sharp estimates of the smallest principal curvature k(1) of level sets of n-dimensional p-harmonic functions which extends the result of 2-dimensional minimal surface case due to Longinetti [Longinetti, On minimal surfaces bounded by two convex curves in parallel planes, J. Differential Equations 67 (3) (1987) 344-358]. More precisely, we prove that the function vertical bar del u vertical bar k(1)(-1) is a convex function with respect to the layer parameter of the level sets for all 2 <= n < + infinity and 1 < p < + infinity. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free