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