Search results for "obol"
showing 10 items of 228 documents
Maximal function estimates and self-improvement results for Poincaré inequalities
2018
Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces. peerReviewed
Dry chlorination of spent nickel metal hydride battery waste for water leaching of battery metals and rare earth elements
2022
An efficient leaching process was developed for nickel, cobalt, and the rare earth elements (REEs) from spent nickel metal hydride (NiMH) battery waste. The process involves dry chlorination with ammonium chloride in low temperature to produce water-soluble chlorinated compounds, followed by simple water leaching. The factors affecting the conversion and solubilization were studied, including the amount of ammonium chloride, residence time and temperature in dry chlorination, and solid to liquid ratio, time and temperature in water leaching. As a result, the dry chlorination process was found to produce ammonium and chloride containing products, depending on the temperature of the process: …
Universal infinitesimal Hilbertianity of sub-Riemannian manifolds
2019
We prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result follows from an embedding of metric derivations into the space of square-integrable sections of the horizontal bundle, which we obtain on all weighted sub-Finsler manifolds. As an intermediate tool, of independent interest, we show that any sub-Finsler distance can be monotonically approximated from below by Finsler ones. All the results are obtained in the general setting of possibly rank-varying structures.
A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space
2020
We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert. Our new approach relies upon the properties of the Alberti-Marchese decomposability bundle. As a consequence of our arguments, we also prove that if the Sobolev norm is closable on compactly-supported smooth functions, then the reference measure is absolutely continuous with respect to the Lebesgue measure.
On the second-order regularity of solutions to the parabolic p-Laplace equation
2022
AbstractIn this paper, we study the second-order Sobolev regularity of solutions to the parabolic p-Laplace equation. For any p-parabolic function u, we show that $$D(\left| Du\right| ^{\frac{p-2+s}{2}}Du)$$ D ( D u p - 2 + s 2 D u ) exists as a function and belongs to $$L^{2}_{\text {loc}}$$ L loc 2 with $$s>-1$$ s > - 1 and $$1<p<\infty $$ 1 < p < ∞ . The range of s is sharp.
Characterization of Cobalt Catalysts on Biomass-Derived Carbon Supports
2017
Cobalt catalysts are known to have a high activity and selectivity in the Fischer–Tropsch reaction converting synthesis gas to higher hydrocarbons (C5+). These catalysts have been supported by different porous materials. Porous carbon materials like activated carbon (AC) have physical and chemical surface properties that affect the preparation of supported metal catalysts and can easily be tailored. In this study, AC was produced by carbonization and steam activation of lignin, a waste fraction from the Kraft pulping process. A series of Co/AC-catalysts was produced and characterized by several techniques. According to the results, tailored properties (high surface area, mesoporosity) were …
Mappings of Lp-integrable distortion: regularity of the inverse
2016
Let be an open set in ℝn and suppose that is a Sobolev homeomorphism. We study the regularity of f–1 under the Lp-integrability assumption on the distortion function Kf. First, if is the unit ball and p > n – 1, then the optimal local modulus of continuity of f–1 is attained by a radially symmetric mapping. We show that this is not the case when p ⩽ n – 1 and n ⩾ 3, and answer a question raised by S. Hencl and P. Koskela. Second, we obtain the optimal integrability results for ∣Df–1∣ in terms of the Lp-integrability assumptions of Kf.
Approximation of W1,p Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian
2018
Let Ω ⊂ R n, n ≥ 4, be a domain and 1 ≤ p 0 on a set of positive measure and Jf < 0 on a set of positive measure. It follows that there are no diffeomorphisms (or piecewise affine homeomorphisms) fk such that fk → f in W1,p . peerReviewed
Stability of the equilibrium state of the equation system of a viscous barotropic gas in the model of atmosphere
2006
We consider the system of equations of viscous gas motion whose pressure is related to the density by the law $p = h \varrho^\gamma$ with 1<γ <2, in a domain defined by two levels of geopotential. Under the force due to geopotential and the Coriolis force, we prove the stability of the equilibrium state in a suitable Sobolev space. Keywords: Viscous barotropic gas, Equilibrium state, Coriolis force Mathematics Subject Classification (2000): 35Q35, 76N15
An Itô Formula for rough partial differential equations and some applications
2020
AbstractWe investigate existence, uniqueness and regularity for solutions of rough parabolic equations of the form $\partial _{t}u-A_{t}u-f=(\dot X_{t}(x) \cdot \nabla + \dot Y_{t}(x))u$ ∂ t u − A t u − f = ( X ̇ t ( x ) ⋅ ∇ + Y ̇ t ( x ) ) u on $[0,T]\times \mathbb {R}^{d}.$ [ 0 , T ] × ℝ d . To do so, we introduce a concept of “differential rough driver”, which comes with a counterpart of the usual controlled paths spaces in rough paths theory, built on the Sobolev spaces Wk,p. We also define a natural notion of geometricity in this context, and show how it relates to a product formula for controlled paths. In the case of transport noise (i.e. when Y = 0), we use this framework to prove a…