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2013-19

Uniform Estimates and Convexity in Capillary Surfaces

by Hans-Christoph Grunau, Stephan Lenor.


Series: 2013-19, Preprints

MSC:
35J66 Nonlinear boundary value problems for nonlinear elliptic equations
35B99 None of the above, but in this section

Abstract:
We prove uniform convexity of solutions to the capillarity boundary value problem for
fixed boundary angle in $(0,pi/2)$ and strictly positive capillarity
constant provided that the base domain $Omegasubset mathbb{R}^2$
is sufficiently close to a disk in a suitable $C^4$-sense.

Keywords:
convexity, capillary surface, domains close to a disk