Local boundedness of weak solutions to elliptic equations with p, q−growth

This article is dedicated to Giuseppe Mingione for his 50th birthday, a leading expert in the regularity theory and in particular in the subject of this manuscript. In this paper we give conditions for the local boundedness of weak solutions to a class of nonlinear elliptic partial differential equations in divergence form of the type considered below in (1.1), under p, q-growth assumptions. The novelties with respect to the mathematical literature on this topic are the general growth conditions and the explicit dependence of the differential equation on u, other than on its gradient Du and on the x variable

Lipschitz regularity for degenerate elliptic integrals with p, q-growth

We establish the local Lipschitz continuity and the higher differentiability of vector-valued local minimizers of a class of energy integrals of the Calculus of Variations. The main novelty is that we deal with possibly degenerate energy densities with respect to the x -variable

Correction: Groundwater circulation and earthquake-related changes in hydrogeological karst environments: a case study of the Sibillini Mountains (central Italy) involving artificial tracers

The original version of this article was revised due to a retrospective Open Access order

Stabilization of the arrival time of a relativistic electron beam to the 50 fs level

We report the results of a low-latency beam phase feed-forward system built to stabilize the arrival time of a relativistic electron beam. The system was operated at the Compact Linear Collider (CLIC) Test Facility (CTF3) at CERN where the beam arrival time was stabilized to approximately 50 fs. The system latency was 350 ns and the correction bandwidth >23 MHz. The system meets the requirements for CLIC.Comment: 5 pages, 9 figures, 1 tabl

On the commutability of homogenization and linearization in finite elasticity

We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor expansion at identity, we prove that the Gamma-limits associated to homogenization and linearization commute. Moreover, we show that the homogenized energy density, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the quadratic term associated to the linearization of the initial energy density

Infants hospitalized for Bordetella pertussis infection commonly have respiratory viral coinfections

Background: Whether viral coinfections cause more severe disease than Bordetella pertussis (B. pertussis) alone remains unclear. We compared clinical disease severity and sought clinical and demographic differences between infants with B. pertussis infection alone and those with respiratory viral coinfections. We also analyzed how respiratory infections were distributed during the 2 years study. Methods: We enrolled 53 infants with pertussis younger than 180 days (median age 58 days, range 17–109 days, 64. 1% boys), hospitalized in the Pediatric Departments at “Sapienza” University Rome and Bambino Gesù Children’s Hospital from August 2012 to November 2014. We tested in naso-pharyngeal washings B. pertussis and 14 respiratory viruses with real-time reverse-transcriptase-polymerase chain reaction. Clinical data were obtained from hospital records and demographic characteristics collected using a structured questionnaire. Results: 28/53 infants had B. pertussis alone and 25 viral coinfection: 10 human rhinovirus (9 alone and 1 in coinfection with parainfluenza virus), 3 human coronavirus, 2 respiratory syncytial virus. No differences were observed in clinical disease severity between infants with B. pertussis infection alone and those with coinfections. Infants with B. pertussis alone were younger than infants with coinfections, and less often breastfeed at admission. Conclusions: In this descriptive study, no associations between clinical severity and pertussis with or without co-infections were found

Second-order L2L^2-regularity in nonlinear elliptic problems

A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the existence and square integrability of the weak derivatives of the nonlinear expression of the gradient under the divergence operator. This provides a nonlinear counterpart of the classical $L^2$-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are established. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required. If the domain is convex, no regularity of its boundary is needed at all