63,016 research outputs found
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 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
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 . 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
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 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
Meson decay in a corrected model
Extensively applied to both light and heavy meson decay and standing as one
of the most successful strong decay models is the model, in which
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 is obtained and applied, as an example, to
and decays.Comment: 3 figures. To appear in Physical Review
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