Article
Licensed
Unlicensed
Requires Authentication
An energy estimate for the difference of solutions for the n-dimensional equation with prescribed mean curvature and removable singularities
-
Stefan Hildebrandt
Published/Copyright:
September 25, 2009
Abstract
We derive an energy bound, estimating a weighted Dirichlet integral of two solutions for the nonparametric equation with prescribed mean curvature in n dimensions in terms of the L1-norm for the difference of their values on the boundary. Furthermore, a similar estimate is established for solutions of the equation divFp(·,∇u)=nH(·,u), where F(x,p) denotes an elliptic Lagrangian with linear growth in p. These results are used to remove singularities of solutions to these equations.
Published Online: 2009-09-25
Published in Print: 2009-07
© by Oldenbourg Wissenschaftsverlag, Cottbus, Germany
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Preface
- Floating criteria in three dimensions
- An energy estimate for the difference of solutions for the n-dimensional equation with prescribed mean curvature and removable singularities
- Plateau’s problem for infinite contours
- Local isometric embedding of two-dimensional Riemannian metrics under geometric initial conditions
- Affine harmonic maps
- Boundary regularity via Uhlenbeck–Rivière decomposition
- Variational Heuristics for Optimal Transportation Maps on Compact Manifolds
Keywords for this article
Removability of singularities;
n-dimensional graphs of prescribed mean curvature
Articles in the same Issue
- Preface
- Floating criteria in three dimensions
- An energy estimate for the difference of solutions for the n-dimensional equation with prescribed mean curvature and removable singularities
- Plateau’s problem for infinite contours
- Local isometric embedding of two-dimensional Riemannian metrics under geometric initial conditions
- Affine harmonic maps
- Boundary regularity via Uhlenbeck–Rivière decomposition
- Variational Heuristics for Optimal Transportation Maps on Compact Manifolds
