Electron. J. Diff. Eqns.,
Vol. 2007(2007), No. 152, pp. 124.
Vertical blow ups of capillary surfaces in
,
Part 1: convex corners
Thalia Jeffres, Kirk Lancaster
Abstract:
One technique which is useful in the calculus of
variations is that of "blowing up". This technique can
contribute to the understanding of the boundary behavior of
solutions of boundary value problems, especially when they involve
mean curvature and a contact angle boundary condition. Our goal in
this note is to investigate the structure of "blown up" sets of
the form
and
when
and
(or
)
minimizes an appropriate functional; sets
like
can be the limits of the blow
ups of subgraphs of solutions of mean curvature problems, for example.
In Part One, we investigate "blown up" sets when the domain has
a convex corner. As an application, we illustrate the second author's
proof of the ConcusFinn Conjecture by providing a simplified proof
when the mean curvature is zero.
Submitted January 9, 2007. Published November 13, 2007.
Math Subject Classifications: 49Q20, 53A10, 76B45.
Key Words: Blowup sets; capillary surface; ConcusFinn conjecture.
Show me the
PDF file (358 KB),
TEX file, and other files for this article.

Thalia Jeffres
Department of Mathematics and Statistics
Wichita State University
Wichita, Kansas, 672600033, USA
email: jeffres@math.wichita.edu 

Kirk Lancaster
Department of Mathematics and Statistics
Wichita State University
Wichita, Kansas, 672600033, USA
email: lancaster@math.wichita.edu 
Return to the EJDE web page