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Abstract Achieving mobile liquid droplets on solid surfaces is crucial for various practical applications, such as self‐cleaning and anti‐fouling coatings. The last two decades have witnessed remarkable progress in designing functional surfaces, including super‐repellent surfaces and lubricant‐infused surfaces, which allow droplets to roll/slide on the surfaces. However, it remains a challenge to enable droplet motion on hydrophilic solid surfaces. In this work, we demonstrate mobile droplets containing ionic surfactants on smooth hydrophilic surfaces that are charged similarly to surfactant molecules. The ionic surfactant‐laden droplets display ultra‐low contact angle and ultra‐low sliding angle simultaneously on the hydrophilic surfaces. The sliding of the droplet is enabled by the adsorbed surfactant ahead of three‐phase contact line, which is regulated by the electrostatic interaction between ionic surfactant and charged solid surface. The droplet can maintain its motion even when the hydrophilic surface has defects. Furthermore, we demonstrate controlled manipulation of ionic surfactant‐laden droplets on hydrophilic surfaces with different patterns. We envision that our simple technique for achieving mobile droplets on hydrophilic surfaces can pave the way to novel slippery surfaces for different applications. 

Abstract In this paper, we study the sharp constants in fractional Sobolev inequalities associated with the regional fractional Laplacian in domains.