Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions

In this article we provide a local wellposedness theory for quasilinear Maxwell equations with absorbing boundary conditions in $\mathcal{H}^m$ for $m \geq 3$. The Maxwell equations are equipped with instantaneous nonlinear material laws leading to a quasilinear symmetric hyperbolic first order system. We consider both linear and nonlinear absorbing boundary conditions. We show existence and uniqueness of a local solution, provide a blow-up criterion in the Lipschitz norm, and prove the continuous dependence on the data. In the case of nonlinear boundary conditions we need a smallness assumption on the tangential trace of the solution. The proof is based on detailed apriori estimates and the regularity theory for the corresponding linear problem which we also develop here.Comment: 43 page

Local wellposedness of quasilinear Maxwell equations with conservative interface conditions

We establish a comprehensive local wellposedness theory for the quasilinear Maxwell system with interfaces in the space of piecewise $H^m$-functions for $m \geq 3$. The system is equipped with instantaneous and piecewise regular material laws and perfectly conducting interfaces and boundaries. We also provide a blow-up criterion in the Lipschitz norm and prove the continuous dependence on the data. The proof relies on precise a priori estimates and the regularity theory for the corresponding linear problem also shown here.Comment: 47 page

Polarization tensors of planar domains as functions of the admittivity contrast

(Electric) polarization tensors describe part of the leading order term of asymptotic voltage perturbations caused by low volume fraction inhomogeneities of the electrical properties of a medium. They depend on the geometry of the support of the inhomogeneities and on their admittivity contrast. Corresponding asymptotic formulas are of particular interest in the design of reconstruction algorithms for determining the locations and the material properties of inhomogeneities inside a body from measurements of current flows and associated voltage potentials on the body's surface. In this work we consider the two-dimensional case only and provide an analytic representation of the polarization tensor in terms of spectral properties of the double layer integral operator associated with the support of simply connected conductivity inhomogeneities. Furthermore, we establish that an (infinitesimal) simply connected inhomogeneity has the shape of an ellipse, if and only if the polarization tensor is a rational function of the admittivity contrast with at most two poles whose residues satisfy a certain algebraic constraint. We also use the analytic representation to provide a proof of the so-called Hashin-Shtrikman bounds for polarization tensors; a similar approach has been taken previously by Golden and Papanicolaou and Kohn and Milton in the context of anisotropic composite materials

Interpolation, embeddings and traces of anisotropic fractional Sobolev spaces with temporal weights

We investigate the properties of a class of weighted vector-valued $L_p$-spaces and the corresponding (an)isotropic Sobolev-Slobodetskii spaces. These spaces arise naturally in the context of maximal $L_p$-regularity for parabolic initial-boundary value problems. Our main tools are operators with a bounded \calH^\infty-calculus, interpolation theory, and operator sums.Comment: This is a preprint version. Published in Journal of Functional Analysis 262 (2012) 1200-122

Faunistic and taxonomic updates on the Tenebrionidae of Malta (Coleoptera)

In the present work, original data is provided for two species of Alleculinae (Tenebrionidae) which were previously omitted from recent works related to this family. The old record of Isomira nitidula is found to be incorrect and should refer to I. melanophthalma. The record of Odocnemis exaratus must be attributed to a different species. Original data is also provided for a new record, Lyphia tetraphylla and for some other previously recorded species. Clamoris crenatus, Stenosis elongata and S. sardoa are excluded from the tenebrionid fauna of Malta whereas the record of Sepidium tricuspidatum tomentosum and Gunarus parvulus requires validation. An alien species, Zophobas opacus, is also recorded but its establishment in Malta cannot be confirmed. A check-list of the 61 species of Tenebrionidae known from Malta is also providedpeer-reviewe

Nd & Hf concentrations and isotopic compositions in the Baltic Sea

Within a process study in the framework of the international GEOTRACES program and led by the Institute of Oceanology of the Polish Academy of Sciences (IOPAN) a two-week cruise on the R/V Oceania sailed in November 2011 to investigate the distribution of trace elements and their isotopes in the Baltic Sea. The scientific goals were particularly focused on compiling trace element budgets for the Baltic Sea including in- and outflow, as well as to investigate elemental behavior and isotopic fractionation associated with the redox gradients of the Baltic Sea water column and the permanently anoxic conditions within its deep basins (i.e. Gotland Deep, Landsort Deep). The Baltic Sea is a shallow, brackish inland sea with an average salinity of ~7 psu in the mixed layer. It is fed by the Bothnian Sea in the north, by the Finland Sea in the east, as well as by numerous rivers from Scandinavia and the Baltic states, and it is drained through the Danish Strait into the North Sea. In the opposite direction, a denser bottom water mass enters the Baltic Sea through deeper channels from the Danish Strait successively filling the deep basins northward. Below 130 m water depth, the water column is permanently anoxic. Here we present the first combined data set of Nd and Hf concentrations and isotopic compositions for the Baltic Sea. A total of 21 water samples (60L volume per sample) including two water column profiles from the deeper basins were filtered (0.45 μm) and Nd and Hf were extracted and analysed following the accepted GEOTRACES protocols. The distribution patterns of the two elements and their isotopic compositions are compared to hydrographic data and oxygen measurements and provide information on sources and mixing of water masses, as well as on exchange processes with the underlying sediments, which are influenced by the prevailing redox gradients