Finite element approximation of the p(⋅)p(\cdot)-Laplacian

We study a~priori estimates for the Dirichlet problem of the $p(\cdot)$-Laplacian, $$-\mathrm{div}(|\nabla v|^{p(\cdot)-2} \nabla v) = f.$$ We show that the gradients of the finite element approximation with zero boundary data converges with rate $O(h^\alpha)$ if the exponent $p$ is $\alpha$-H\"{o}lder continuous. The error of the gradients is measured in the so-called quasi-norm, i.e. we measure the $L^2$-error of $|\nabla v|^{\frac{p-2}{2}} \nabla v$

Approximation properties of the qq-sine bases

For $q>12/11$ the eigenfunctions of the non-linear eigenvalue problem associated to the one-dimensional $q$-Laplacian are known to form a Riesz basis of $L^2(0,1)$. We examine in this paper the approximation properties of this family of functions and its dual, in order to establish non-orthogonal spectral methods for the $p$-Poisson boundary value problem and its corresponding parabolic time evolution initial value problem. The principal objective of our analysis is the determination of optimal values of $q$ for which the best approximation is achieved for a given $p$ problem.Comment: 20 pages, 11 figures and 2 tables. We have fixed a number of typos and added references. Changed the title to better reflect the conten

Adaptive FE-BE Coupling for Strongly Nonlinear Transmission Problems with Coulomb Friction

We analyze an adaptive finite element/boundary element procedure for scalar elastoplastic interface problems involving friction, where a nonlinear uniformly monotone operator such as the p-Laplacian is coupled to the linear Laplace equation on the exterior domain. The problem is reduced to a boundary/domain variational inequality, a discretized saddle point formulation of which is then solved using the Uzawa algorithm and adaptive mesh refinements based on a gradient recovery scheme. The Galerkin approximations are shown to converge to the unique solution of the variational problem in a suitable product of L^p- and L^2-Sobolev spaces.Comment: 27 pages, 3 figure

Improve Management of acute heart failure with ProcAlCiTonin in EUrope:results of the randomized clinical trial IMPACT EU Biomarkers in Cardiology (BIC) 18

Aim: To determine whether initiation of antibiotic therapy (ABX) by procalcitonin (PCT) within 8 h of admission in patients presenting to the emergency department with symptoms and signs of acute heart failure (AHF) and elevated natriuretic peptides would improve clinical outcomes. Methods and results: The study was a randomized multicentre clinical trial conducted at 16 sites in Europe. Patients were randomized to either a PCT-guided strategy or standard care. Patients with PCT-guided strategy (n = 370) had ABX initiated if PCT was > 0.2 μg/L. Patients with standard care (n = 372) had AHF care in accordance with published guidelines without PCT. The primary endpoint was 90-day all-cause mortality. Pre-specified secondary endpoints included 30-day all-cause mortality and readmission and rate of pneumonia. The Data Safety and Review Committee recommended stopping the study for futility when 762 of the planned 792 patients had been enrolled. A total of 742 patients could be analysed. Patients were elderly (median age: 77 years), 38% were women, and had typical signs and symptoms of AHF. All-cause mortality at 90 days was 10.3% in the PCT-guided group vs. 8.2% in standard care (P = 0.316). Thirty-day readmission was significantly higher in the PCT-guided group vs. standard care but the difference vanished until day 90. The rate of pneumonia was overall low (7.5%) and not different between groups. Conclusions: In patients with AHF, a strategy of PCT-guided initiation of ABX was not more effective than a standard care strategy in improving clinical outcomes

Optimal Sobolev regularity for linear second-order divergence elliptic operators occurring in real-world problems

On bounded three-dimensional domains, we consider divergence-type operators including mixed homogeneous Dirichlet and Neumann boundary conditions and discontinuous coefficient functions. We develop a geometric framework in which it is possible to prove that the operator provides an isomorphism of suitable function spaces. In particular, in these spaces, the gradient of solutions turns out to be integrable with exponent larger than the space dimension three. Relevant examples from real-world applications are provided in great detail

Nonsmooth analysis of doubly nonlinear evolution equations

In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy functional,for existence of solutions to the related Cauchy problem. We prove our main existence result by passing to the limit in a time-discretization scheme with variational techniques. Finally, we discuss an application to a material model in finite-strain elasticity.Comment: 45 page

C-Jun N-terminal kinase (JNK) isoforms play differing roles in otitis media

BACKGROUND: Innate immunity and tissue proliferation play important roles in otitis media (OM), the most common disease of childhood. CJUN terminal kinase (JNK) is potentially involved in both processes. RESULTS: Genes involved in both innate immune and growth factor activation of JNK are upregulated during OM, while expression of both positive and negative JNK regulatory genes is altered. When compared to wildtypes (WTs), C57BL/6 mice deficient in JNK1 exhibit enhanced mucosal thickening, with delayed recovery, enhanced neutrophil recruitment early in OM, and delayed bacterial clearance. In contrast, JNK2(−/−) mice exhibit delayed mucosal hyperplasia that eventually exceeds that of WTs and is slow to recover, delayed recruitment of neutrophils, and failure of bacterial clearance. CONCLUSIONS: The results suggest that JNK1 and JNK2 play primarily opposing roles in mucosal hyperplasia and neutrophil recruitment early in OM. However, both isoforms are required for the normal resolution of middle ear infection. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12865-014-0046-z) contains supplementary material, which is available to authorized users