# A Generalization of "Existence and Behavior of the Radial Limits of a Bounded Capillary Surface at a Corner"

## TL;DR

This paper extends the existence theorem and bounds on side fans for bounded capillary surfaces at corners to cases with variable contact angles approaching 0 or π, broadening the applicability of prior results.

## Contribution

It generalizes previous theorems to include variable contact angles that are not bounded away from 0 and π, for both convex and nonconvex corners.

## Key findings

- Extended existence theorem to variable contact angles.
- Generalized bounds on side fans for new contact angle conditions.
- Applicable to both convex and nonconvex corners.

## Abstract

The principle existence theorem (i.e. Theorem 1) of "Existence and Behavior of the Radial Limits of a Bounded Capillary Surface at a Corner" (Pacific J. Math. Vol. 176, No. 1 (1996), 165-194) is extended to the case of a contact angle $\gamma$ which is not bounded away from $0$ and $\pi$ (and depends on position in a bounded domain $\Omega\in {\bf R}^{2}$ with a convex corner at ${\cal O}=(0,0)$). The lower bound on the size of "side fans" (i.e. Theorem 2 in the above paper) is extended to case of such contact angles for convex and nonconvex corners.