Dietary habits are associated with the prevalence of type 2 diabetes: a study among a middle eastern population. [PDF]
J Nutr Sci, 2022 Mahdi S +7 more
europepmc +1 more source
Nonlinear Muckenhoupt-Wheeden type bounds on Reifenberg flat domains, with applications to quasilinear Riccati type equations [PDF]
arXiv, 2013 A weighted norm inequality of Muckenhoupt-Wheeden type is obtained for gradients of solutions to a class of quasilinear equations with measure data on Reifenberg flat domains. This essentially leads to a resolution of an existence problem for quasilinear Riccati type equations with a gradient source term of arbitrary power law growth.
arxiv
Global Maximizers for the Sphere Adjoint Fourier Restriction Inequality [PDF]
arXiv, 2013 We show that constant functions are global maximizers for the adjoint Fourier restriction inequality for the sphere.
arxiv
G-Convergence, Dirichlet to Neumann maps and invisibility [PDF]
arXiv, 2013 We establish optimal conditions under which the G-convergence of linear elliptic operators implies the convergence of the corresponding Dirichlet to Neumann maps. As an application we show that the approximate cloaking isotropic materials from [ Greenleaf, A.; Kurylev, Y.; Lassas, M.; Uhlmann, G. Approximate quantum and acoustic cloaking. J.
arxiv
On variants of $H$-measures and compensated compactness [PDF]
arXiv, 2014 We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we present new compensated compactness results for quadratic functionals in the case of general pseudo-differential ...
arxiv
Two dimensional water waves in holomorphic coordinates II: global solutions [PDF]
arXiv, 2014 This article is concerned with the infinite depth water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates,and prove that small localized data leads to global solutions. This article is a continuation of authors' earlier paper arXiv:1401.1252.
arxiv
Hardy's inequality for functions vanishing on a part of the boundary [PDF]
arXiv, 2014 We develop a geometric framework for Hardy's inequality on a bounded domain when the functions do vanish only on a closed portion of the boundary.
arxiv
Sharp Hardy-Littlewood-Sobolev Inequalities on Octonionic Heisenberg Group [PDF]
arXiv, 2014 This paper is a second one following our work [CLZ13] in series, considering sharp Hardy- Littlewood-Sobolev inequalities on groups of Heisenberg type. The first important breakthrough was made by Frank and Lieb in [FL12]. In this paper, analogous results are obtained for octonionic Heisenberg group.
arxiv
Boundedness of propagators for Dirac equations with potentials on Wiener amalgam spaces [PDF]
arXivIn this paper we prove boundedness of propagators for Dirac equations with unbounded time-dependent potentials on Wiener amalgam spaces. In particular we deal with class of potentials such as including Stark and harmonic potentials.
arxiv
Approximation of elliptic equations with BMO coefficients [PDF]
arXiv, 2014 We study solution techniques for elliptic equations in divergence form, where the coefficients are only of bounded mean oscillation (BMO). For $|p-2|<\varepsilon$ and a right hand side in $W^{-1}_p$ we show convergence of a finite element scheme, where $\varepsilon$ depends on the oscillation of the coefficients.
arxiv