Boundary Harnack estimates in slit domains and applications to thin free boundary problems

We provide a higher order boundary Harnack inequality for harmonic functions in slit domains. As a corollary we obtain the $C^\infty$ regularity of the free boundary in the Signorini problem near non-degenerate points

The Voltammetric Study of the Reduction of Tetraalkylammonium Perchlorate by Fe(TPP)\u3csup\u3e2-\u3c/sup\u3e

Tetraalkylammonium ions react with Fe(TPP)2− to form Fe(TPP)(R)− and trialkylamine. The tetrabutylammonium cation was verified to be the source of the alkyl group in the product, Fe(TPP)(R)−, by using (1H5C2)3(2H5C2)N− as the cation and 2H NMR. The reaction of Fe(TPP)2− with Bu4N− was monitored by cyclic voltammetry and thin layer spectroelectrochemistry. The activation parameters were measured, and were most consistent with an electron transfer (ET) mechanism. The rate of the reaction of tetramethyl and tetraethylammonium ions with Fe(TPP)2− was also examined. The rate constant decreased significantly as the carbon chain length decreased, which was also consistent with an ET mechanism

The two membranes problem for different operators

We study the two membranes problem for different operators, possibly nonlocal. We prove a general result about the H\"older continuity of the solutions and we develop a viscosity solution approach to this problem. Then we obtain $C^{1,\gamma}$ regularity of the solutions provided that the orders of the two operators are different. In the special case when one operator coincides with the fractional Laplacian, we obtain the optimal regularity and a characterization of the free boundary

Regularity in a one-phase free boundary problem for the fractional Laplacian

For a one-phase free boundary problem involving a fractional Laplacian, we prove that "flat free boundaries" are $C^{1,\alpha}$. We recover the regularity results of Caffarelli for viscosity solutions of the classical Bernoulli-type free boundary problem with the standard Laplacian.Comment: Corrected some typo

Meson decay in a corrected 30P3^P_0 model

Extensively applied to both light and heavy meson decay and standing as one of the most successful strong decay models is the $3^P_0$ model, in which $q\bar{q}$ pair production is the dominant mechanism. The pair production can be obtained from the non-relativistic limit of a microscopic interaction Hamiltonian involving Dirac quark fields. The evaluation of the decay amplitude can be performed by a diagrammatic technique for drawing quark lines. In this paper we use an alternative approach which consists in a mapping technique, the Fock-Tani formalism, in order to obtain an effective Hamiltonian starting from same microscopic interaction. An additional effect is manifest in this formalism associated to the extended nature of mesons: bound-state corrections. A corrected $3^P_0$ is obtained and applied, as an example, to $b_{1}\to\omega\pi$ and $a_{1}\to\rho\pi$ decays.Comment: 3 figures. To appear in Physical Review