Global Lipschitz Regularity for a Class of Quasilinear Elliptic Equations

The Lipschitz continuity of solutions to Dirichlet and Neumann problems for nonlinear elliptic equations, including the p-Laplace equation, is established under minimal integrability assumptions on the data and on the curvature of the boundary of the domain. The case of arbitrary bounded convex domains is also included. The results have new consequences even for the Laplacian.     

Concentration-compactness principles for Moser–Trudinger inequalities: new results and proofs

We are concerned with the best exponent in Concentration-Compactness principles for the borderline case of the Sobolev inequality. We present a new approach, which both yields a rigorous proof of the relevant principle in the standard case when functions vanishing on the boundary are considered, and enables us to deal with functions with unrestricted boundary values.     

Generation of GW radiation pulses from a VUV free-electron laser operating in the femtosecond regime

Experimental results are presented from vacuum-ultraviolet free-electron laser (FEL) operating in the self-amplified spontaneous emission (SASE) mode. The generation of ultrashort radiation pulses became possible due to specific tailoring of the bunch charge distribution. A complete characterization of the linear and nonlinear modes of the SASE FEL operation was performed. At saturation the FEL produces ultrashort pulses (30-100 fs FWHM) with a peak radiation power in the GW level and with full transverse coherence. The wavelength was tuned in the range of 95-105 nm.     

Interpretation of the Mössbauer spectra of oxyhemoglobin in terms of a low lying excited state

It is shown how the temperature evolution of the Mössbauer spectra of oxyhemoglobin can be explained by means of an excited triplet state at about 150 K above the ground state. The agreement is particularly good for temperatures T ≤ 180 K.     

Sobolev embeddings into spaces of Campanato, Morrey, and Hölder type

Necessary and sufficient conditions on a rearrangement-invariant Banach function space X(Q) on a cube Q in , n?2, are given for the corresponding Sobolev space W¹X(Q) to be continuously embedded into (generalized) Campanato, Morrey, or Hölder spaces. The optimal such r.i. spaces X(Q) are found. As a by-product, sharp inclusion relations are proved among Campanato, Morrey, and Hölder type spaces.     

High-gain harmonic-generation free-electron laser seeded by harmonics generated in gas

The injection of a seed in a free-electron laser (FEL) amplifier reduces the saturation length and improves the longitudinal coherence. A cascaded FEL, operating in the high-gain harmonic-generation regime, allows us to extend the beneficial effects of the seed to shorter wavelengths. We report on the first operation of a high-gain harmonic-generation free-electron laser, seeded with harmonics generated in gas. The third harmonics of a Ti:sapphire laser, generated in a gas cell, has been amplified and up-converted to its second harmonic (λ(rad)=133 nm) in a FEL cascaded configuration based on a variable number of modulators and radiators. We studied the transition between coherent harmonic generation and superradiant regime, optimizing the laser performances with respect to the number of modulators and radiators.     

Moser-Trudinger trace inequalities

Sharp constants in exponential inequalities involving a general class of measures in domains Ω⊂Rn are exhibited in the limiting case of the Sobolev embedding theorem. A comprehensive approach is presented yielding, as special instances, trace inequalities on ∂Ω, on smooth submanifolds of Ω of arbitrary dimension, and also on fractal subsets of Ω, and recovering, in particular, the classical Moser-Trudinger inequality.     

Measurement of the Anisotropy of the Lamb–Mössbauer Factor in EuBa2Cu3O7

Hyperfine Interactions - The lattice dynamics of high-Tc EuBCO superconductor was studied by means of Mössbauer spectroscopy of the 151Eu ion in samples with oriented grains. Three samples...     

Optimal summability of solutions to nonlinear elliptic problems

The strongest possible norms in a priori estimates for solutions to a class of second-order nonlinear elliptic boundary value problems are exhibited.     

Study of the [Fe(OMe)(dpm)2]2 dimer in the presence of a magnetic field by using Mössbauer spectroscopy

We present a Mössbauer study of a S = 0 ground state magnetic Fe(III)-dimer in the presence of an applied 5 T longitudinal magnetic field, between 7.6 and 33 K. The values obtained for the isomer shift and the quadrupolar splitting are comparable with the ones of Fe(III) ions coordinated to eight oxygen ions. Regarding the spin dynamics, both intramultiplet and intermultiplet transitions are considered. In the chosen temperature range the rate of the former transitions is constant, within the errors, while the rate of the latter ones quickly increases with the temperature.