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Uniform Estimates and Convexity in Capillary Surfaces

by Hans-Christoph Grunau, Stephan Lenor.

Series: 2013-19, Preprints

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

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.

convexity, capillary surface, domains close to a disk