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

The pyrrolizidine alkaloid senecionine induces CYP-dependent destruction of sinusoidal endothelial cells and cholestasis in mice

Pyrrolizidine alkaloids (PAs) are widely occurring phytotoxins which can induce severe liver damage in humans and other mammalian species by mechanisms that are not fully understood. Therefore, we investigated the development of PA hepatotoxicity in vivo, using an acutely toxic dose of the PA senecionine in mice, in combination with intravital two-photon microscopy, histology, clinical chemistry, and in vitro experiments with primary mouse hepatocytes and liver sinusoidal endothelial cells (LSECs). We observed pericentral LSEC necrosis together with elevated sinusoidal marker proteins in the serum of senecionine-treated mice and increased sinusoidal platelet aggregation in the damaged tissue regions. In vitro experiments showed no cytotoxicity to freshly isolated LSECs up to 500 µM senecionine. However, metabolic activation of senecionine by preincubation with primary mouse hepatocytes increased the cytotoxicity to cultivated LSECs with an EC50 of approximately 22 µM. The cytochrome P450 (CYP)-dependency of senecionine bioactivation was confirmed in CYP reductase-deficient mice where no PA-induced hepatotoxicity was observed. Therefore, toxic metabolites of senecionine are generated by hepatic CYPs, and may be partially released from hepatocytes leading to destruction of LSECs in the pericentral region of the liver lobules. Analysis of hepatic bile salt transport by intravital two-photon imaging revealed a delayed uptake of a fluorescent bile salt analogue from the hepatic sinusoids into hepatocytes and delayed elimination. This was accompanied by transcriptional deregulation of hepatic bile salt transporters like Abcb11 or Abcc1. In conclusion, senecionine destroys LSECs although the toxic metabolite is formed in a CYP-dependent manner in the adjacent pericentral hepatocytes.</p

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

Myeloid Differentiation Primary Response Gene 88 Is Required for the Resolution of Otitis Media

Signaling defects in the Toll-like receptor (TLR) pathway, such as interleukin-1 receptor–associated kinase 4 deficiency, highlight the prominence of TLR signaling in the defense against bacterial disease. Because myeloid differentiation primary response gene 88 (MyD88) can transduce signals from almost all TLRs, we studied its role in otitis media (OM), the most common upper respiratory tract bacterial infectious disease in young children

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