Riesz potentials and nonlinear parabolic equations

The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation. Heat kernels type estimates persist in the nonlinear cas

Fractional differentiability for solutions of nonlinear elliptic equations

We study nonlinear elliptic equations in divergence form $${\operatorname{div}}{\mathcal A}(x,Du)={\operatorname{div}}G.$$ When ${\mathcal A}$ has linear growth in $Du$, and assuming that $x\mapsto{\mathcal A}(x,\xi)$ enjoys $B^\alpha_{\frac{n}\alpha, q}$ smoothness, local well-posedness is found in $B^\alpha_{p,q}$ for certain values of $p\in[2,\frac{n}{\alpha})$ and $q\in[1,\infty]$. In the particular case ${\mathcal A}(x,\xi)=A(x)\xi$, $G=0$ and $A\in B^\alpha_{\frac{n}\alpha,q}$, $1\leq q\leq\infty$, we obtain $Du\in B^\alpha_{p,q}$ for each $p<\frac{n}\alpha$. Our main tool in the proof is a more general result, that holds also if ${\mathcal A}$ has growth $s-1$ in $Du$, $2\leq s\leq n$, and asserts local well-posedness in $L^q$ for each $q>s$, provided that $x\mapsto{\mathcal A}(x,\xi)$ satisfies a locally uniform $VMO$ condition

Quality properties of caraway seed from various sources

A köménymag minőségi értékelésére alkalmas módszereket tanulmányozták különböző forrásokból származó 11 minta: külföldi és finn kereskedelmi minták és vadon termett finn minták alapján. A vizsgálati módszerek felölelték a szennyezésekre vonatkozó előzetes szemlét a külső megjelenés alapján a zamat és a nagyság, a súlyveszteség (nedvességtartalom), a hamu és a savban oldhatatlan hamu, az illóolaj-tartalom meghatározását és az illóolajban a karvon és limonén tartalom meghatározását gázkromatográfiával. Ezenkívül érzékszervi módszerekkel értékelték az illatok küszöbértékeit és a zamatanyagok jellegét. Tárgyalják ezeknek a módszereknek a használhatóságát. A vadon termett köménymagmintákban az illóolaj-tartalom kifejezetten nagyobb volt, mint az egyéb mintákban. A vadon termett magminták illatküszöbei azonban csak átlagosak voltak. A régi mintákban a zamatveszteség nem volt határozott, és a zamatanyagok jellege élesebben kömény típusú volt, mint a frissebb mintákban. Tárgyalják továbbá a vad kömény termesztési lehetőségeit Finnországban. Auf Grund 11 Muster unterschiedlicher Herkunft: und zwar auf Grund ausländischer und finnischer kommerziellen Muster und wild gewachsenen finnischen Muster wurden Methoden studiert, die zur Qualitätsbewertung von Kümmelkörnern geeignet sind. Die Untersuchungsmethoden umfassten eine vorangehende Besichtigung bezüglich der Verunreinigungen auf Grund der äusseren Erscheinung, ferner die Bestimmung des Aromas und der Grösse, des Gewichtsverlustes (Feuchtigkeitsgehaltes), des Äschegehaltes und der Menge der in Säure unlöslichen Asche, die Bestimmung des ätherischen Ölgehaltes und des Gehaltes and Carvon und Limonen in ätherischen Öl durch Gaschromatographie. Ausserdem wurden die Schwellenwerte des Geruchs und der Charakter der Aromatoffe mittels sensorischen Methoden bewertet. Die Verwendbarkeit dieser Methoden wird besprochen. In den wild gewachsenen Kiimmelkörnermustern war der Gehalt an ätherischem öl ausgesprochen höher als in den übrigen Mustern. Die Schwellenwerte des Geruchs waren jedoch in den Mustern der wild gewachsenen Kümmelkörner nur durchschnittlich. In den älteren Mustern war der Aromaverlust nicht ausdrücklich, und der Charakter der Aromastoffe wies einen schärferen Kümmeltyp auf, als in den frischeren Mustern. Ferner werden die Anbaumöglichkeiten des wilden Kümmels in Finnland erörtert

Surveillance of endemic foci of tick-borne encephalitis in Finland 1995-2013 : evidence of emergence of new foci

The geographical risk areas for tick-borne encephalitis (TBE) in Finland remained the same until the beginning of the 21st century, but a considerable geographical expansion has been observed in the past 10 years. In order to support public health measures, the present study describes the number of laboratory-confirmed TBE cases and laboratory tests conducted and the associated trends by hospital district, with a particular emphasis on the suspected geographical risk areas. An additional investigation was conducted on 1,957 clinical serum samples throughout the country taken from patients with neurological symptoms to screen for undiagnosed TBE cases. This study identified new TBE foci in Finland, reflecting the spread of the disease into new areas. Even in the most endemic municipalities, transmission of TBE to humans occurred in very specific and often small foci. The number of antibody tests for TBE virus more than doubled (an increase by 105%) between 2007 and 2013. Analysis of the number of tests also revealed areas in which the awareness of clinicians may be suboptimal at present. However, it appears that underdiagnosis of neuroinvasive TBE is not common.Peer reviewe

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

Respiratory diphtheria in an asylum seeker from Afghanistan arriving to Finland via Sweden, December 2015

In December 2015, an asylum seeker originating from Afghanistan was diagnosed with respiratory diphtheria in Finland. He arrived in Finland from Sweden where he had already been clinically suspected and tested for diphtheria. Corynebacterium diphtheriae was confirmed in Sweden and shown to be genotypically and phenotypically toxigenic. The event highlights the importance of early case detection, rapid communication within the country and internationally as well as preparedness plans of diphtheria antitoxin availability.Peer reviewe