University of Texas at Austin

About: University of Texas at Austin is a education organization based out in Austin, Texas, United States. It is known for research contribution in the topics: Population & Poison control. The organization has 94352 authors who have published 206297 publications receiving 9070052 citations. The organization is also known as: UT-Austin & UT Austin.

Regularity of the obstacle problem for a fractional power of the laplace operator

Abstract: Given a function ϕ and s ∈ (0, 1), we will study the solutions of the following obstacle problem: • u ≥ ϕ in R n , • (−� ) s u ≥ 0i nR n , • (−� ) s u(x) = 0 for those x such that u(x )>ϕ (x), • lim|x|→+∞ u(x) = 0. We show that when ϕ is C 1,s or smoother, the solution u is in the space C 1,α for every α< s. In the case where the contact set {u = ϕ} is convex, we prove the optimal regularity result u ∈ C 1,s . When ϕ is only C 1,β for a β< s, we prove that our solution u is C 1,α for every α< β. c � 2006 Wiley Periodicals, Inc.

Large-Area Graphene Single Crystals Grown by Low-Pressure Chemical Vapor Deposition of Methane on Copper

Abstract: Graphene single crystals with dimensions of up to 0.5 mm on a side were grown by low-pressure chemical vapor deposition in copper-foil enclosures using methane as a precursor. Low-energy electron microscopy analysis showed that the large graphene domains had a single crystallographic orientation, with an occasional domain having two orientations. Raman spectroscopy revealed the graphene single crystals to be uniform monolayers with a low D-band intensity. The electron mobility of graphene films extracted from field-effect transistor measurements was found to be higher than 4000 cm2 V−1 s−1 at room temperature.