Regularity of capillarity droplets with obstacle

TL;DR

This paper investigates the regularity of capillarity droplets constrained by obstacles, providing insights relevant to nanowire growth models and advancing understanding of capillarity phenomena with boundary constraints.

Contribution

It introduces new regularity results for $ ext{Lambda}$-minimizers of capillarity energy with obstacle constraints, applicable to nanowire growth modeling.

Findings

Established regularity properties of capillarity droplets with obstacles.

Connected mathematical results to nanowire growth applications.

Extended understanding of capillarity energy minimizers in constrained settings.

Abstract

In this paper we study the regularity properties of $\Lambda$-minimizers of the capillarity energy in a half space with the wet part constrained to be confined inside a given planar region. Applications to a model for nanowire growth are also provided.