Boundary Regularity for Minimal Graphs of Higher Codimensions

Qi Ding , Yuanlong Xin

Chinese Annals of Mathematics, Series B ›› 2022, Vol. 43 ›› Issue (5) : 869 -876.

PDF
Chinese Annals of Mathematics, Series B ›› 2022, Vol. 43 ›› Issue (5) : 869 -876. DOI: 10.1007/s11401-022-0364-z
Article

Boundary Regularity for Minimal Graphs of Higher Codimensions

Author information +
History +
PDF

Abstract

In this paper, the authors derive Hölder gradient estimates for graphic functions of minimal graphs of arbitrary codimensions over bounded open sets of Euclidean space under some suitable conditions.

Keywords

Boundary regularity / Minimal graphs / Higher condimension / Bernstein type theorem

Cite this article

Download citation ▾
Qi Ding, Yuanlong Xin. Boundary Regularity for Minimal Graphs of Higher Codimensions. Chinese Annals of Mathematics, Series B, 2022, 43(5): 869-876 DOI:10.1007/s11401-022-0364-z

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Benjamin S T. The maximal graph Dirichlet problem in semi-Euclidean spaces. Comm. Anal. Geom., 2012, 20(2): 255-270

[2]

Ding Q. Liouville type theorems for minimal graphs over manifolds. Analysis & PDE, 2021, 14(6): 1925-1949

[3]

Ding, Q., Jost, J. and Xin, Y. L., Minimal graphs of arbitrary codimension in Euclidean space with bounded 2-dilation, arXiv: 2021, 2109.09383.

[4]

Gilbarg D, Trudinger N. Elliptic Partial Differential Equations of Second Order, 1983, Berlin-New York: Springer-Verlag

[5]

Jenkins H, Serrin J. The Dirichlet problem for the minimal surface equation in higher dimension. J. Reine Angew. Math., 1968, 229: 170-187

[6]

Jost J, Xin Y L. Bernstein type theorems for higher codimension. Calc. Var., 1999, 9: 277-296

[7]

Jost J, Xin Y L, Yang L. The Gauss image of entire graphs of higher codimension and Bernstein type theorems. Calc. Var. Partial Differential Equations, 2013, 47(3–4): 711-737

[8]

Jost J, Xin Y L, Yang L. A spherical Bernstein theorem for minimal submanifolds of higher codimension. Calc. Var. Partial Differential Equations, 2018, 57(6): 21

[9]

Krylov N V. Lectures on Elliptic and Parabolic Equations in Sobolev Spaces, Graduate Studies in Mathematics, 2008, Providence, Rhode Island: American Mathematical Society Volume 96

[10]

Lawson H, Osserman R. Non-existence, non-uniqueness and irregularity of solutions to the minimal surface system. Acta Math., 1977, 139: 1-17

[11]

Simon, L., Lectures on Geometric Measure Theory, Proceedings of the center for mathematical analysis, Australian National University, Vol. 3, 1983.

[12]

Lieberman G M. Second Order Parabolic Differential Equations, 1996, River Edge, N.J.: World Scientific

[13]

Morrey C B. Second Order Elliptic Systems of Differential Equations, Contributions to the Theory of Partial Differential Equation. Annals of Math. Studies, 1954, Princeton: Princeton U. Press 33

[14]

Morrey C B. Multiple Integrals in the Calculus of Variations, 1966, N.Y.: Springer-Verlag

[15]

Osserman R. Minimal varieties. Bull. Amer. Math. Soc., 1969, 75: 1092-1120

AI Summary AI Mindmap
PDF

112

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/