Exponential elliptic boundary value problems on a solid torus in the critical of supercritical case

In this paper we investigate the behavior and the existence of positive and non-radially symmetric solutions to nonlinear exponential elliptic model problems defined on a solid torus $\bar{T}$ of $\mathbb{R}^3$, when data are invariant under the group $G=O(2)\times I \subset O(3)$. The model problems of interest are stated below: {ll} {\bf(P_1)} & \displaystyle \Delta\upsilon+\gamma=f(x)e^\upsilon, \upsilon>0\quad \mathrm{on} \quad T, \quad\upsilon |_{_{\partial T}}=0. and {ll}\bf{(P_2)} & \displaystyle \Delta\upsilon+a+fe^\upsilon=0, \upsilon>0\quad \mathrm{on}\quad T, [1.3ex] &\displaystyle \frac{\partial \upsilon}{\partial n}+b+ge^\upsilon=0\quad \mathrm{on} \quad{\partial T}. We prove that exist solutions which are $G-$invariant and these exhibit no radial symmetries. In order to solve the above problems we need to find the best constants in the Sobolev inequalities in the exceptional case

“God is Hidden in the Earthly Kingdom:” The Lutheran Two-Kingdoms Theory as Foundation of Scandavanian Secularity

Martin Luther’s signature “two kingdoms” teaching of the sixteenth century was an early and innovative theory of secularization that lies at the heart of historical Scandinavian culture. Defying the organic medieval models of Western Christendom, Luther separated the heavenly and earthly kingdoms, the saint and the sinner, faith and reason, church and the state, Gospel and the Law, as well as the spiritual and secular uses of law, government and authority. Though God is separated from day-to-day life, Luther wrote, God is still hidden in the earthly kingdom” and can be seen through various “masks,” “mists,” and “mimes.” Though the visible church is separated from the state and other institutions, religion remains pervasive in the common callings of every person to be God’s prophet, priest and king in every vocation and location of life. Luther’s two kingdoms theory is a complicated and controversial part of this thinking, but it is worth re-exploring today as pluralistic Scandinavia faces strong new pressures of both sacralization and secularization and seeks to discern anew “the hidden sacraliity of the secular.

Linguistic Naturalism and Natural Style. From Varro and Cicero to Dionysius of Halicarnassus

NWO276-30-009Classics and Classical Civilizatio

Die Milchversorgung in Württemberg

- Inhalt #8- Das Milchversorgungsgebiet #9- Die Milcherzeugung #16- Die Milchverwertung #30- Der Absatz von Frischmilch, Insbesondere der Eisenbahnversand in Milch und der Genossenschaftlicher Milchabsatz #44- Die polizeiliche milchkontrolle #56- Die milchpreise #76- Der milchtarif #90- Die stadtische milchversorgung #95- Schlutz #12