Minimum principles and a priori estimates for some translating soliton type problems

被引：2

作者：

Enache, Cristian ^{[1
]}

Lopez, Rafael ^{[2
]}

机构：

[1] Amer Univ Sharjah, Dept Math & Stat, Univ City Rd,POB 26666, Sharjah, U Arab Emirates

[2] Univ Granada, Dept Geometria & Topol, Inst Matemat IEMath GR, E-18071 Granada, Spain

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2019年 / 187卷

关键词：

Mean curvature flow; Translating solitons; Critical points; Nodal lines; Maximum principles; A priori estimates; MEAN-CURVATURE EQUATION; DIRICHLET PROBLEM; EVOLUTION; HYPERSURFACES; SINGULARITIES; SURFACES; FLOW;

D O I：

10.1016/j.na.2019.05.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we are dealing with two classes of mean curvature type problems that generalize the translating soliton problem. A first result proves that the solutions to these problems have unique interior critical points. Using this uniqueness result, we next derive a priori C-0 and C-1 estimates for the solutions to these problems, by means of some minimum principles for appropriate P-functions, in the sense of L. E. Payne. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：352 / 364

页数：13

共 33 条

[1] [Anonymous], SOME ASPECTS MECH 1
[2] [Anonymous], 1979, Nonlinear Anal., Theory, Methods & Appl., DOI DOI 10.1016/0362-546X(79)90076-2
[3] Barbu L, 2013, Z ANGEW MATH PHYS, V64, P321, DOI 10.1007/s00033-012-0240-x
[4] Bergner M., 2008, ANAL MUNICH, V28, P149
[5] EIGENFUNCTIONS AND NODAL SETS
CHENG, SY
[J]. COMMENTARII MATHEMATICI HELVETICI, 1976, 51 (01) : 43 - 55
[6] Enache C, 2015, P AM MATH SOC, V143, P309
[7] MAXIMUM AND MINIMUM PRINCIPLES FOR A CLASS OF MONGE-AMPERE EQUATIONS IN THE PLANE, WITH APPLICATIONS TO SURFACES OF CONSTANT GAUSS CURVATURE
Enache, Cristian
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2014, 13 (03) : 1347 - 1359
[8] Gilbarg D., 1983, Grundlehren der mathematischen Wissenschaften, V2nd
[9] Isoperimetry of waists and concentration of maps
Gromov, M
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2003, 13 (01) : 178 - 215
[10] Mean curvature flow singularities for mean convex surfaces
Huisken, G
Sinestrari, C
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1999, 8 (01) : 1 - 14

← 1 2 3 4 →