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The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one -phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions n >= 3 is completely open. In this context, axial ...
Tolerancing is an important step toward the fabrication of high-quality and cost-effective lens surfaces. It is critical for wafer-level optics, when up to tens of thousands microlenses are fabricated in parallel and whose surfaces cannot be formed individ ...
We study the regularity of the regular and of the singular set of the obstacle problem in any dimension. Our approach is related to the epiperimetric inequality of Weiss (Invent Math 138:23-50, Wei99a), which works at regular points and provides an alterna ...
A method for creating a watertight boundary between two graphical elements including the steps of displaying a first surface having a first shape and a second surface having a second shape on the display, an open space existing between the first surface an ...
When a fluid-immersed array of supported plates or pillars is dried, evaporation leads to the formation of menisci on the tips of the plates or pillars that bring them together to form complex patterns. Building on prior experimental observations, we use a ...
We identify the multilayered compound GeBi4Te7 to be a topological insulator with a Dirac point slightly above the valence band maximum, using angle-resolved photoemission spectroscopy (ARPES) measurements. The spin polarization satisfies the time reversal ...
We establish basic local existence as well as a stability result concerning small perturbations of the Catenoid minimal surface in R-3 under hyperbolic vanishing mean curvature flow. ...
We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient di ...
In an attempt to go beyond the conventional laboratory experiments widely reported in literature around the emerging technique of soil bio-cementation, this work addresses key challenges related to its large-scale application. Precisely, a state-of-the-art ...
When a fluid-immersed array of supported plates or pillars is dried, evaporation leads to the formation of menisci on the tips of the plates or pillars that bring them together to form complex patterns. Building on prior experimental observations, we use a ...
