A threshold phenomenon for embeddings of H0mH^m_0 into Orlicz spaces

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H^m_0$-norms of the functions is greater than or equal to a positive geometric constant.Comment: 14 Page

The policy of "critical dialogue" : an analysis of European human rights policy towards Iran from 1992 to 1997

This paper analyses the European Union’s policy of ‘critical dialogue’ with Iran from 1992 to 1997. Based on a ‘constructivist’ approach it is claimed that the ‘critical dialogue’ resulted from the increasing importance of human rights in the Union’s Common Foreign and Security Policy. The ‘critical dialogue’ attempted to change Iranian behaviour and strengthen ‘moderate’ forces in Iran by keeping a dialogue on human rights, the fatwa against Salman Rushdie, the Iranian stance on the Arab-Israeli Peace Process, and Iran’s alleged support for terrorism. Although the ‘dialogue’ produced little tangible results, structural changes both in Iranian domestic and foreign policy give evidence that the ‘dialogue’ has been partly successful. The ‘critical dialogue’ was suspended in 1997 after a German court found the Iranian leadership guilty of or¬dering to assassinate four members of the Iranian-Kurdish opposition in Berlin. In contrast to the EU the United States pursued a policy of ‘containing’ Iran through economic sanctions. The policy differed from the European concept both in means and priorities. While the EU’s primary concern was Iran’s internal human rights conduct and its regional behaviour, U.S.-policy focused on alleged Iranian support for terrorism, its quest for weapons of mass destruction, and its opposition to the Peace Process. In 1995 the United States imposed a unilateral trade-embargo against Iran and in 1996 sanctions against companies investing in the Iranian oil-sector. The election of the ‘moderate’ President Khatami and the following ‘opening’ in Iran’s domestic and foreign policies led to a complete reassessment of European and American policies. The EU initiated a ‘comprehensive dialogue’ emphasising its previous concerns, while the U.S. government seeks a ‘genuine reconciliation’ with Iran, mainly to re-vitalise economic relations and to integrate Iran into the security-structure in the Gulf. Due to the inherent differences in their approaches, however, a com¬mon Euro-American policy towards Iran seems unlikely

Global pointwise decay estimates for defocusing radial nonlinear wave equations

We prove global pointwise decay estimates for a class of defocusing semilinear wave equations in $n=3$ dimensions restricted to spherical symmetry. The technique is based on a conformal transformation and a suitable choice of the mapping adjusted to the nonlinearity. As a result we obtain a pointwise bound on the solutions for arbitrarily large Cauchy data, provided the solutions exist globally. The decay rates are identical with those for small data and hence seem to be optimal. A generalization beyond the spherical symmetry is suggested.Comment: 9 pages, 1 figur

A convergent and constraint-preserving finite element method for the p-harmonic flow into spheres

Published versio

Multiple solutions of the quasirelativistic Choquard equation

We prove existence of multiple solutions to the quasirelativistic Choquard equation with a scalar potential

The Construction of a Partially Regular Solution to the Landau-Lifshitz-Gilbert Equation in R2\mathbb{R}^2

We establish a framework to construct a global solution in the space of finite energy to a general form of the Landau-Lifshitz-Gilbert equation in $\mathbb{R}^2$. Our characterization yields a partially regular solution, smooth away from a 2-dimensional locally finite Hausdorff measure set. This construction relies on approximation by discretization, using the special geometry to express an equivalent system whose highest order terms are linear and the translation of the machinery of linear estimates on the fundamental solution from the continuous setting into the discrete setting. This method is quite general and accommodates more general geometries involving targets that are compact smooth hypersurfaces.Comment: 43 pages, 2 figure

Quantization for an elliptic equation of order 2m with critical exponential non-linearity

On a smoothly bounded domain $\Omega\subset\R{2m}$ we consider a sequence of positive solutions $u_k\stackrel{w}{\rightharpoondown} 0$ in $H^m(\Omega)$ to the equation $(-\Delta)^m u_k=\lambda_k u_k e^{mu_k^2}$ subject to Dirichlet boundary conditions, where $0<\lambda_k\to 0$. Assuming that $$\Lambda:=\lim_{k\to\infty}\int_\Omega u_k(-\Delta)^m u_k dx<\infty,$$ we prove that $\Lambda$ is an integer multiple of \Lambda_1:=(2m-1)!\vol(S^{2m}), the total $Q$-curvature of the standard $2m$-dimensional sphere.Comment: 33 page

Existence of solutions to a higher dimensional mean-field equation on manifolds

For $m\geq 1$ we prove an existence result for the equation $$(-\Delta_g)^m u+\lambda=\lambda\frac{e^{2mu}}{\int_M e^{2mu}d\mu_g}$$ on a closed Riemannian manifold $(M,g)$ of dimension $2m$ for certain values of $\lambda$.Comment: 15 Page