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 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

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

Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis

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

New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces

We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.Comment: to appear in GAF

An improved geometric inequality via vanishing moments, with applications to singular Liouville equations

We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical singularities and Onsager's description of turbulence. We analyse the problem of existence variationally, and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the Moser-Trudinger inequality, and in turn to lower bounds on the Euler-Lagrange functional. We then discuss existence and non-existence results.Comment: some references adde

Distinguishing N-acetylneuraminic acid linkage isomers on glycopeptides by ion mobility-mass spectrometry

Differentiating the structure of isobaric glycopeptides represents a major challenge for mass spectrometry-based characterisation techniques. Here we show that the regiochemistry of the most common N-acetylneuraminic acid linkages of N-glycans can be identified in a site-specific manner from individual glycopeptides using ion mobility-mass spectrometry analysis of diagnostic fragment ions