Parabolic oblique derivative problem in generalized Morrey spaces

We study the regularity of the solutions of the oblique derivative problem for linear uniformly parabolic equations with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized Morrey space than the strong solution belongs to the corresponding generalized Sobolev-Morrey space

On the L_p-solvability of higher order parabolic and elliptic systems with BMO coefficients

We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be merely measurable in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders. For the proof, we develop a set of new techniques to produce mean oscillation estimates for systems on a half space.Comment: 44 pages, introduction revised, references expanded. To appear in Arch. Rational Mech. Ana

A note on boundedness of operators in Grand Grand Morrey spaces

In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces. We prove a kind of \textit{reduction lemma} which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder\'on-Zygmund operators in the framework of grand grand Morrey spaces.Comment: 8 page

UV-Optical Pixel Maps of Face-On Spiral Galaxies -- Clues for Dynamics and Star Formation Histories

UV and optical images of the face-on spiral galaxies NGC 6753 and NGC 6782 reveal regions of strong on-going star formation that are associated with structures traced by the old stellar populations. We make NUV--(NUV-I) pixel color-magnitude diagrams (pCMDs) that reveal plumes of pixels with strongly varying NUV surface brightness and nearly constant I surface brightness. The plumes correspond to sharply bounded radial ranges, with (NUV-I) at a given NUV surface brightness being bluer at larger radii. The plumes are parallel to the reddening vector and simple model mixtures of young and old populations, thus neither reddening nor the fraction of the young population can produce the observed separation between the plumes. The images, radial surface-brightness, and color plots indicate that the separate plumes are caused by sharp declines in the surface densities of the old populations at radii corresponding to disk resonances. The maximum surface brightness of the NUV light remains nearly constant with radius, while the maximum I surface brightness declines sharply with radius. An MUV image of NGC 6782 shows emission from the nuclear ring. The distribution of points in an (MUV-NUV) vs. (NUV-I) pixel color-color diagram is broadly consistent with the simple mixture model, but shows a residual trend that the bluest pixels in (MUV-NUV) are the reddest pixels in (NUV-I). This may be due to a combination of red continuum from late-type supergiants and [SIII] emission lines associated with HII regions in active star-forming regions. We have shown that pixel mapping is a powerful tool for studying the distribution and strength of on-going star formation in galaxies. Deep, multi-color imaging can extend this to studies of extinction, and the ages and metallicities of composite stellar populations in nearby galaxies.Comment: LaTeX with AASTeX style file, 29 pages with 12 figures (some color, some multi-part). Accepted for publication in The Astrophysical Journa

Partial Schauder estimates for second-order elliptic and parabolic equations

We establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving H\"older semi-norms not with respect to all, but only with respect to some of the independent variables.Comment: CVPDE, accepted (2010)

The prognostic value of the myeloid-mediated immunosuppression marker Arginase-1 in classic Hodgkin Lymphoma

Neutrophilia is hallmark of classic Hodgkin Lymphoma (cHL), but its precise characterization remains elusive. We aimed at investigating the immunosuppressive role of high-density neutrophils in HL

Sharp two-sided heat kernel estimates for critical Schr\"odinger operators on bounded domains

On a smooth bounded domain \Omega \subset R^N we consider the Schr\"odinger operators -\Delta -V, with V being either the critical borderline potential V(x)=(N-2)^2/4 |x|^{-2} or V(x)=(1/4) dist (x,\partial\Omega)^{-2}, under Dirichlet boundary conditions. In this work we obtain sharp two-sided estimates on the corresponding heat kernels. To this end we transform the Scr\"odinger operators into suitable degenerate operators, for which we prove a new parabolic Harnack inequality up to the boundary. To derive the Harnack inequality we have established a serier of new inequalities such as improved Hardy, logarithmic Hardy Sobolev, Hardy-Moser and weighted Poincar\'e. As a byproduct of our technique we are able to answer positively to a conjecture of E.B.Davies.Comment: 40 page

SF3B1-mutated chronic lymphocytic leukemia shows evidence of NOTCH1 pathway activation including CD20 downregulation

Chronic lymphocytic leukemia (CLL) is characterized by a low CD20 expression, in part explained by an epigenetic-driven downregulation triggered by mutations of the NOTCH1 gene. In the present study, by taking advantage of a wide and well-characterized CLL cohort (n=537), we demonstrate that CD20 expression is downregulated in SF3B1-mutated CLL in an extent similar to NOTCH1-mutated CLL. In fact, SF3B1-mutated CLL cells show common features with NOTCH1-mutated CLL cells, including a gene expression profile enriched of NOTCH1-related gene sets and elevated expression of the active intracytoplasmic NOTCH1. Activation of the NOTCH1 signaling and down-regulation of surface CD20 in SF3B1-mutated CLL cells correlate with over-expression of an alternatively spliced form of DVL2, a component of the Wnt pathway and negative regulator of the NOTCH1 pathway. These findings are confirmed by separately analyzing the CD20-dim and CD20-bright cell fractions from SF3B1-mutated cases as well as by DVL2 knock-out experiments in CLL-like cell models. Altogether, the clinical and biological features that characterize NOTCH1-mutated CLL may also be recapitulated in SF3B1-mutated CLL, contributing to explain the poor prognosis of this CLL subset and providing the rationale for expanding novel agents-based therapies to SF3B1-mutated CLL

A limit model for thermoelectric equations

We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both spatial and temperature dependent transport coefficients under some real boundary conditions in accordance with the Seebeck-Peltier-Thomson cross-effects. Our first purpose is that the existence of a weak solution holds true under minimal assumptions on the data, as in particular nonsmooth domains. Two existence results are studied under different assumptions on the electrical conductivity. Their proofs are based on a fixed point argument, compactness methods, and existence and regularity theory for elliptic scalar equations. The second purpose is to show the existence of a limit model illustrating the asymptotic situation.Comment: 20 page