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

(Lattice) Propagators and Extraction of Spectral Densities

In this proceeding, we explain a few steps for an alternative extraction of the spectral density of a two-point function (propagator) based on a discrete set of data points. We present a so-called Tikhonov regularization of this particular inverse problem. We test it on 2 cases: lattice 0++} glueball data and mock gluon data.Comment: 8 pages, 4 figures. Proceedings of Xth Quark Confinement and the Hadron Spectrum, October 8-12, 2012, TUM Campus Garching, Munich, German

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

Evaluation of a Pound Net Leader Designed to Reduce Sea Turtle Bycatch

Offshore pound net leaders in the southern portion of Chesapeake Bay in Virginia waters were documented to incidentally take protected loggerhead, Caretta caretta, and Kemp’s ridley, Lepidochelys kempii, sea turtles. Because of these losses, NOAA’s National Marine Fisheries Service (NMFS) in 2004 closed the area to offshore pound net leaders annually from 6 May to 15 July and initiated a study of an experimental leader design that replaced the top two-thirds of the traditional mesh panel leader with vertical ropes (0.95 cm) spaced 61 cm apart. This experimental leader was tested on four pound net sites on the eastern shore of Chesapeake Bay in 2004 and 2005. During the 2 trial periods, 21 loggerhead and Kemp’s ridley sea turtles were found interacting with the control leader and 1 leatherback turtle, Dermochelys coriacea, was found interacting with the experimental leader. Results of a negative binomial regression analysis comparing the two leader designs found the experimental leader significantly reduced sea turtle interactions (p=0.03). Finfish were sampled from the pound nets in the study to assess finfish catch performance differences between the two leader designs. Although the conclusions from this element of the experiment are not robust, paired t-test and Wilcoxon signed rank test results determined no significant harvest weight difference between the two leaders. Kolmogorov-Smirnov tests did not reveal any substantive size selectivity differences between the two leaders

Scattering theory for a class of non-selfadjoint extensions of symmetric operators

This work deals with the functional model for a class of extensions of symmetric operators and its applications to the theory of wave scattering. In terms of Boris Pavlov's spectral form of this model, we find explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices. On the basis of these formulae, we are able to construct wave operators and derive a new representation for the scattering matrix for pairs of such extensions in both self-adjoint and non-self-adjoint situations.Comment: 32 pages; This is the continuation of arXiv:1703.06220 (and formerly contained in v1); this version is as accepted by the journal (Operator Theory: Advances and Applications