Search results for "Estimates"
showing 10 items of 72 documents
On Lp resolvent estimates for Laplace–Beltrami operators on compact manifolds
2014
In this article we prove Lp estimates for resolvents of Laplace–Beltrami operators on compact Riemannian manifolds, generalizing results of Kenig, Ruiz and Sogge (1987) in the Euclidean case and Shen (2001) for the torus. We follow Sogge (1988) and construct Hadamard's parametrix, then use classical boundedness results on integral operators with oscillatory kernels related to the Carleson and Sjölin condition. Our initial motivation was to obtain Lp Carleman estimates with limiting Carleman weights generalizing those of Jerison and Kenig (1985); we illustrate the pertinence of Lp resolvent estimates by showing the relation with Carleman estimates. Such estimates are useful in the constructi…
Partial data inverse problems for Maxwell equations via Carleman estimates
2015
In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim-Uhlmann and Kenig-Sj\"ostrand-Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.
Direct chromatographic study of the enantioselective biodegradation of ibuprofen and ketoprofen by an activated sludge
2018
[EN] The quantification of the enantiomeric fraction (EF) during the biodegradation process is essential for environmental risk assessment. In this paper the enantioselective biodegradation of ibuprofen, IBU, and ketoprofen, KET, two of the drugs most consumed, was evaluated. Biodegradation experiments were performed in batch mode using a minimal salts medium inoculated with an activated sludge (collected from a Valencian Waste Water Treatment Plant) and supplemented with the racemate of each compound. The inoculum activity was verified using fluoxetine as reference compound. The experimental conditions used (analyte concentration and volume of inoculum) were chosen according to OECD guidel…
Estimating global injuries morbidity and mortality
2020
Background. While there is a long history of measuring death and disability from injuries, modern research methods must account for the wide spectrum of disability that can occur in an injury, and must provide estimates with sufficient demographic, geographical and temporal detail to be useful for policy makers. The Global Burden of Disease (GBD) 2017 study used methods to provide highly detailed estimates of global injury burden that meet these criteria. Methods. In this study, we report and discuss the methods used in GBD 2017 for injury morbidity and mortality burden estimation. In summary, these methods included estimating cause-specific mortality for every cause of injury, and then est…
Short-Term Effects of Air Pollution on Cardiovascular Hospitalizations in the Pisan Longitudinal Study
2021
Air pollution effects on cardiovascular hospitalizations in small urban/suburban areas have been scantly investigated. Such effects were assessed among the participants in the analytical epidemiological survey carried out in Pisa and Cascina, Tuscany, Italy (2009–2011). Cardiovascular hospitalizations from 1585 subjects were followed up (2011–2015). Daily mean pollutant concentrations were estimated through random forests at 1 km (particulate matter: PM10, 2011–2015
Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems
2015
This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed
Error Estimates for a Class of Elliptic Optimal Control Problems
2016
In this article, functional type a posteriori error estimates are presented for a certain class of optimal control problems with elliptic partial differential equation constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state equation. The functional a posteriori error estimates developed by Repin in the late 1990s are applied to estimate the cost function value from both sides without requiring the exact solution of the state equation. Moreover, a lower bound for the minimal cost functional value is derived. A meaningful error quantity coinciding with the gap between the cost functional values of an arbitrary admissible …
On the shape of compact hypersurfaces with almost constant mean curvature
2015
The distance of an almost constant mean curvature boundary from a finite family of disjoint tangent balls with equal radii is quantitatively controlled in terms of the oscillation of the scalar mean curvature. This result allows one to quantitatively describe the geometry of volume-constrained stationary sets in capillarity problems.
Gradient estimates for heat kernels and harmonic functions
2020
Let $(X,d,\mu)$ be a doubling metric measure space endowed with a Dirichlet form $\E$ deriving from a "carr\'e du champ". Assume that $(X,d,\mu,\E)$ supports a scale-invariant $L^2$-Poincar\'e inequality. In this article, we study the following properties of harmonic functions, heat kernels and Riesz transforms for $p\in (2,\infty]$: (i) $(G_p)$: $L^p$-estimate for the gradient of the associated heat semigroup; (ii) $(RH_p)$: $L^p$-reverse H\"older inequality for the gradients of harmonic functions; (iii) $(R_p)$: $L^p$-boundedness of the Riesz transform ($p<\infty$); (iv) $(GBE)$: a generalised Bakry-\'Emery condition. We show that, for $p\in (2,\infty)$, (i), (ii) (iii) are equivalent, wh…
Partial data inverse problems for the Hodge Laplacian
2017
We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth order potential. The method is based on Carleman estimates for the Hodge Laplacian with relative or absolute boundary conditions, and on the construction of complex geometric optics solutions which reduce the Calderon type problem to a tensor tomography problem for 2-tensors. The arguments in this paper allow to establish partial data results for elliptic systems that generalize the scalar resu…