On the Capillarity Equation in Two Dimensions

TL;DR

This paper investigates the global behavior of solutions to the two-dimensional capillarity equation, revealing new constraints on solutions that were previously uncharacterized in existing literature.

Contribution

It provides a novel analysis of the capillarity equation's solutions, focusing on their global properties independent of boundary conditions.

Findings

Solutions are constrained in ways not previously characterized.

New global behavior constraints for the capillarity equation.

Insights into solution structure without boundary condition dependence.

Abstract

We study the capillarity equation from the global point of view of behavior of its solutions without explicit regard to boundary conditions. We show its solutions to be constrained in ways, that have till now not been characterized in literature known to us.