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Volume 25, Issue 3
Gaussian Curvature Estimates for the Convex Level Sets of Solutions for Some Nonlinear Elliptic Partial Differential Equations

Peihe Wang & Wei Zhang

J. Part. Diff. Eq., 25 (2012), pp. 239-275.

Published online: 2012-09

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  • Abstract

We give lower bound estimates for the Gaussian curvature of convex level sets of minimal surfaces and the solutions to semilinear elliptic equations in terms of the norm of boundary gradient and the Gaussian curvature of the boundary.

  • Keywords

Gaussian curvature estimates convex level sets minimal surface semilinear elliptic equation maximum principle

  • AMS Subject Headings

35B45, 35J93, 35J61, 35J05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

peihewang@hotmail.com (Peihe Wang)

wei.zhang@anu.edu.au (Wei Zhang)

  • BibTex
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  • TXT
@Article{JPDE-25-239, author = {Peihe and Wang and peihewang@hotmail.com and 4469 and School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China and Peihe Wang and Wei and Zhang and wei.zhang@anu.edu.au and 12137 and Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT 0200, Australia and Wei Zhang}, title = {Gaussian Curvature Estimates for the Convex Level Sets of Solutions for Some Nonlinear Elliptic Partial Differential Equations}, journal = {Journal of Partial Differential Equations}, year = {2012}, volume = {25}, number = {3}, pages = {239--275}, abstract = {

We give lower bound estimates for the Gaussian curvature of convex level sets of minimal surfaces and the solutions to semilinear elliptic equations in terms of the norm of boundary gradient and the Gaussian curvature of the boundary.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v25.n3.4}, url = {http://global-sci.org/intro/article_detail/jpde/5186.html} }
TY - JOUR T1 - Gaussian Curvature Estimates for the Convex Level Sets of Solutions for Some Nonlinear Elliptic Partial Differential Equations AU - Wang , Peihe AU - Zhang , Wei JO - Journal of Partial Differential Equations VL - 3 SP - 239 EP - 275 PY - 2012 DA - 2012/09 SN - 25 DO - http://doi.org/10.4208/jpde.v25.n3.4 UR - https://global-sci.org/intro/article_detail/jpde/5186.html KW - Gaussian curvature estimates KW - convex level sets KW - minimal surface KW - semilinear elliptic equation KW - maximum principle AB -

We give lower bound estimates for the Gaussian curvature of convex level sets of minimal surfaces and the solutions to semilinear elliptic equations in terms of the norm of boundary gradient and the Gaussian curvature of the boundary.

Peihe Wang & Wei Zhang. (2019). Gaussian Curvature Estimates for the Convex Level Sets of Solutions for Some Nonlinear Elliptic Partial Differential Equations. Journal of Partial Differential Equations. 25 (3). 239-275. doi:10.4208/jpde.v25.n3.4
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