On convexity of level sets of p-harmonic functions

Ting Zhang; Wei Zhang

doi:10.1016/j.jde.2013.06.004

On convexity of level sets of p-harmonic functions

Ting Zhang, Wei Zhang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper, we give sharp estimates of the smallest principal curvature k₁ 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 |∇;u|k1-1 is a convex function with respect to the layer parameter of the level sets for all 2≤n<+∞ and 1<p<+∞.

Original language	English
Pages (from-to)	2065-2081
Number of pages	17
Journal	Journal of Differential Equations
Volume	255
Issue number	7
DOIs	https://doi.org/10.1016/j.jde.2013.06.004
Publication status	Published - 1 Oct 2013

Access to Document

10.1016/j.jde.2013.06.004

Cite this

@article{4d16bb7d47ab4a958e30e924d8bc7324,

title = "On convexity of level sets of p-harmonic functions",

abstract = "In this paper, we give sharp estimates of the smallest principal curvature k1 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 |∇;u|k1-1 is a convex function with respect to the layer parameter of the level sets for all 2≤n<+∞ and 1",

keywords = "Curvature estimates, Maximum principle, P-Harmonic functions, Support function",

author = "Ting Zhang and Wei Zhang",

year = "2013",

month = oct,

day = "1",

doi = "10.1016/j.jde.2013.06.004",

language = "English",

volume = "255",

pages = "2065--2081",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "7",

}

TY - JOUR

T1 - On convexity of level sets of p-harmonic functions

AU - Zhang, Ting

AU - Zhang, Wei

PY - 2013/10/1

Y1 - 2013/10/1

N2 - In this paper, we give sharp estimates of the smallest principal curvature k1 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 |∇;u|k1-1 is a convex function with respect to the layer parameter of the level sets for all 2≤n<+∞ and 1

AB - In this paper, we give sharp estimates of the smallest principal curvature k1 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 |∇;u|k1-1 is a convex function with respect to the layer parameter of the level sets for all 2≤n<+∞ and 1

KW - Curvature estimates

KW - Maximum principle

KW - P-Harmonic functions

KW - Support function

UR - http://www.scopus.com/inward/record.url?scp=84880513968&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2013.06.004

DO - 10.1016/j.jde.2013.06.004

M3 - Article

SN - 0022-0396

VL - 255

SP - 2065

EP - 2081

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 7

ER -

On convexity of level sets of p-harmonic functions

Abstract

Access to Document

Other files and links

Fingerprint

Cite this