The Mean Curvature Measure

@inproceedings{Dai2009TheMC,
  title={The Mean Curvature Measure},
  author={Qiuyi Dai and Neil S. Trudinger and Xujia Wang},
  year={2009}
}
We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a sharp Harnack inequality for the minimal surface equation, which is crucial for our proof of the weak continuity. As an application we prove the existence of weak solutions to the… CONTINUE READING

References

Publications referenced by this paper.
SHOWING 1-10 OF 22 REFERENCES

Serrin, The strong maximum principle revisited

J. P. Pucci
  • J. Diff. Eqns
  • 2004

Labutin, Potential estimates for a class of fully nonlinear elliptic equations

D. A. Lab
  • Duke Math. J
  • 2002

Serrin, The Harnack inequality in R2 for quasilinear elliptic equations

J. P. Pucci
  • J. Anal. Math.,
  • 2001

Soner, Level set approach to mean curvature flow in arbitrary codimension

H. M. AS L. Ambrosio
  • J. Diff. Geom
  • 1996