Global Estimates for Quasilinear Elliptic Equations on Reifenberg Flat Domains

New global regularity estimates are obtained for solutions to a class of quasilinear elliptic boundary value problems. The coefficients are assumed to have small BMO seminorms, and the boundary of the domain is sufficiently flat in the sense of Reifenberg. The main regularity estimates obtained are in weighted Lorentz spaces. Other regularity results in Lorentz–Morrey, Morrey, and Hölder spaces are shown to follow from the main estimates.     

Photochemical decoration of silver nanoparticles on magnetic microspheres as substrates for the detection of adenine by surface-enhanced Raman scattering

In this work, silver nanoparticles (AgNPs) decorated magnetic microspheres (MMs) are prepared as surface-enhanced Raman scattering (SERS) substrate for the analysis of adenine in aqueous solutions. To prepare these substrates, magnetic particles were first synthesized by coprecipitation of Fe(II) and Fe(III) with ammonium hydroxide. A thin layer of cross-linked polymer was formed on these magnetic particles by polymerization through suspension of magnetic particles into a solution of divinyl benzene/methyl methacrylate. The resulted polymer protected magnetic particles are round in shape with a size of 80 μm in diameter. To form AgNPs on these MMs, photochemical reduction method was employed and the factors in photochemical reduction method were studied and optimized for the preparation of highly sensitive and stable AgNPs on MMs substrates (abbreviated as AgMMs substrates). By dispersing the AgMMs in aqueous samples, cylindrical magnet was used to attract the AgMMs for SERS detections. The observed enhancement factor of AgMMs reached 7 orders in magnitude for detection of adenine with a detection limit approaching to few hundreds of nanomolar.