310 research outputs found
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
Singularities of Nonlinear Elliptic Systems
Through Morrey's spaces (plus Zorko's spaces) and their potentials/capacities
as well as Hausdorff contents/dimensions, this paper estimates the singular
sets of nonlinear elliptic systems of the even-ordered Meyers-Elcrat type and a
class of quadratic functionals inducing harmonic maps.Comment: 18 pages Communications in Partial Differential Equation
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
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)
Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth
We establish global regularity for weak solutions to quasilinear divergence
form elliptic and parabolic equations over Lipschitz domains with controlled
growth conditions on low order terms. The leading coefficients belong to the
class of BMO functions with small mean oscillations with respect to .Comment: 24 pages, to be submitte
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
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