Boundary Harnack inequality and a priori estimates of singular solutions of quasilinear elliptic equations

We extend some classical results dealing with boundary Harnack inequatilities to a class of quasilinear elliptic equations and derive some new estimates for solutions of such equations with an isolated singularity on the boundary of a domain.Comment: 17 page

The "red shelf" of the Hb line in the Seyfert 1 galaxies RXS J01177+3637 and HS 0328+05

A few Seyfert 1s have a Hb profile with a red wing usually called the "red shelf". The most popular interpretation of this feature is that it is due to broad redshifted lines of Hb and [OIII]4959,5007; we have observed two Seyfert 1s displaying a "red shelf" and showed that in these two objects the main contributor is most probably the HeI 4922,5016 lines having the velocity and width of the broad Hb component. There is no evidence for the presence of a broad redshifted component of Hb or [OIII] in any of these two objects.Comment: LaTeX file (uses AA vers. 5.1 class, enclosed), 8 pages, 9 figures. Accepted for publication in Astronomy & Astrophysics. Also available at http://www.obs-hp.fr/www/preprints.htm

Miscellaneous observations of active galactic nuclei. II

We observed 37 AGN candidates and classified them on the basis of their spectroscopic properties; three are confirmed QSOs, one is a BL Lac object, nine are Seyfert 1 galaxies, four Seyfert 2s, while twenty are HII regions.Comment: LaTeX 2e, 15 pages (4 tables and 9 .eps figures included in text). Uses L-AA 3.0, epsf.tex and psfig.sty (not included). Accepted to appear in A&

What Can and Cannot Be Done about Rating Agencies

The constantly developing global financial system needs better risk assessments than Credit Rating Agencies (CRAs) have been collectively able to deliver during recent crises. More comprehensive public disclosure by issuers on their financial risks, which would not require intermediation by CRAs, is the best chance for new and better risk assessment methodologies and practices to emerge. To put it in a simplistic but concise way, what is needed is "a John Moody for the 21st century." CRAs themselves can perhaps be somewhat improved by adequate regulation and supervision, but public policy initiatives that focus only on CRAs are unlikely to adequately address the need for substantially better financial risk assessments. If real progress is to be made towards a better public understanding of financial risks, it will have to involve innovative approaches that even well-regulated CRAs, on the basis of recent experience, may not be the best placed to deliver.

Keeping the Promise of Global Accounting Standards

In this Policy Brief, PIIE Visiting Fellow Nicolas Véron provides a comprehensive analysis of the strategic challenges facing the attempt to harmonize the world's accounting practices through the global spread of International Financial Reporting Standards (IFRS). After taking stock of the initial successes of IFRS adoption, he identifies unsustainable features in the current governance framework of the IFRS Foundation, the organization that hosts IFRS standard-setting, and advocates reform to make the IFRS Foundation accountable not only to individual governments but also to the global investor community. He also proposes a variety of incentives for individual jurisdictions to converge towards IFRS, as such convergence looks set to be more gradual than had been envisaged by the IFRS Foundation in the past.

Financial Reform after the Crisis: An Early Assessment

This working paper aims to take stock of global efforts towards financial reform since the start of the financial crisis in 2007–08 and to provide a synthetic (if simplified) picture of their status as of January 2012. Underlying dynamics are described and analyzed both at the global level (particularly G-20, International Monetary Fund, and the Financial Stability Board) and in individual jurisdictions, as well as the impact the crisis has had on these regions. The possible next steps of financial reform are then reviewed, including: the ongoing crisis management in Europe, the new emphasis on macroprudential approaches, the challenges posed by globally integrated financial firms, the implementation of harmonized global standards, and the links between financial systems and growth.banks, financial regulation, global financial crisis, global governance, international standards

Semilinear fractional elliptic equations with gradient nonlinearity involving measures

We study the existence of solutions to the fractional elliptic equation (E1) $(-\Delta)^\alpha u+\epsilon g(|\nabla u|)=\nu$ in a bounded regular domain $\Omega$ of $\R^N (N\ge2)$, subject to the condition (E2) $u=0$ in $\Omega^c$, where $\epsilon=1$ or $-1$, $(-\Delta)^\alpha$ denotes the fractional Laplacian with $\alpha\in(1/2,1)$, $\nu$ is a Radon measure and $g:\R_+\mapsto\R_+$ is a continuous function. We prove the existence of weak solutions for problem (E1)-(E2) when $g$ is subcritical. Furthermore, the asymptotic behavior and uniqueness of solutions are described when $\nu$ is Dirac mass, $g(s)=s^p$, $p\geq 1$ and $\epsilon=1$.Comment: \`a para\^itre, J. Funct. Ana

Singular solutions of fractional elliptic equations with absorption

The aim of this paper is to study the singular solutions to fractional elliptic equations with absorption \left\{\arraycolsep=1pt \begin{array}{lll} (-\Delta)^\alpha u+|u|^{p-1}u=0,\quad & \rm{in}\quad\Omega\setminus\{0\},\\[2mm] u=0,\quad & \rm{in}\quad \R^N\setminus\Omega,\\[2mm] \lim_{x\to 0}u(x)=+\infty, \end{array} \right. where $p>0$, $\Omega$ is an open, bounded and smooth domain of $\R^N\ (N\ge2)$ with $0\in\Omega$. We analyze the existence, nonexistence, uniqueness and asymptotic behavior of the solutions