Constructing graphs over $R^n$ with small prescribed mean-curvature

Details Constructing graphs over $R^n$ with small prescribed mean-curvature Constructing graphs over $R^n$ with small prescribed mean-curvature

2010-09-08

arxiv.org/abs/1009.1435v3

Mathematics

Analysis of PDEs

27 pages, LaTeX, one reference added. Submitted for publication

Scientific paper

In this paper a convergent series expansion is constructed to solve the prescribed mean curvature equation for n-dimensional hypersurfaces in n+1 dimensional Euclidean or Minkowskian space(time) which are graphs of a smooth real function u, and whose mean curvature function H is not too large in Hoelder norm, and integrable. Our approach is inspired by the Maxwell-Born-Infeld theory of electromagnetism in Minkowski spacetime, for which our method yields the first systematic way of explicitly computing the electrostatic potential u for regular charge densities proportional to H and small Born parameter. Therefore, after the general n-dimensional problems have been treated with the help of nonlinear Hodge theory and Banach algebra estimates, our approach is reworked in more detail for n=3.

Affiliated with

Also associated with

No associations

Rating

Constructing graphs over $R^n$ with small prescribed mean-curvature does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Constructing graphs over $R^n$ with small prescribed mean-curvature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Constructing graphs over $R^n$ with small prescribed mean-curvature will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-31584