Recursos de colección
Gómez
,
Tomás L.; Sols
,
Ignacio
For a connected reductive group $G$, we generalize the notion of
(semi)stable Higgs $G$-bundles on curves to smooth projective
schemes of higher dimension, allowing also Higgs $G$-sheaves, and
construct the corresponding moduli space.
Bethuel
,
Fabrice; Jerrard
,
Robert L.; Smets
,
Didier
We derive the asymptotical dynamical law for Ginzburg-Landau
vortices in the plane under the Schrödinger dynamics, as the
Ginz\-burg-Landau parameter goes to zero. The limiting law is the
well-known point-vortex system. This result extends to the whole
plane previous results of [Colliander, J.E. and Jerrard, R.L.:
Vortex dynamics for the Ginzburg-Landau-Schrödinger equation.
Internat. Math. Res. Notices 1998, no. 7, 333-358; Lin, F.-H. and Xin, J.\,X.:
On the incompressible fluid limit and the vortex motion law of the nonlinear
Schr\"{o}dinger equation. Comm. Math. Phys. 200 (1999), 249-274] established for bounded
domains, and holds for arbitrary degree at infinity. When this
degree is non-zero, the total Ginzburg-Landau energy is infinite.
Hajłasz
,
Piotr; Koskela
,
Pekka; Tuominen
,
Heli
We study necessary and sufficient conditions for a domain to be a
Sobolev extension domain in the setting of metric measure spaces.
In particular, we prove that extension domains must satisfy a
measure density condition.
Henk
,
Martin; Hernández Cifre
,
María A.
We study the location and the size of the roots of Steiner
polynomials of convex bodies in the Minkowski relative geometry.
Based on a problem of Teissier on the intersection numbers of
Cartier divisors of compact algebraic varieties it was conjectured
that these roots have certain geometric properties related to the
in- and circumradius of the convex body. We show that the roots of
1-tangential bodies fulfill the conjecture, but we also present
convex bodies violating each of the conjectured properties.
Jaikin-Zapirain
,
Andrei
Let $p$ be a prime. It is proved that a non-trivial word $w$ from a
free group $F$ has finite width in every finitely generated pro-$p$
group if and only if $w\not \in (F^\prime)^{p} F^{\prime\prime}$.
Also it is shown that any word $w$ has finite width in a compact
$p$-adic group.
Arcoya
,
David; Martínez-Aparicio
,
Pedro J.
We study the existence of positive solution $w\in H_0^1(\Omega)$
of the quasilinear equation $-\Delta w+ g(w)|\nabla w|^2=a(x)$,
$x\in \Omega$, where $\Omega$ is a bounded domain in
$\mathbb R^N$, $0\leq a\in L^\infty (\Omega )$ and $g$
is a nonnegative continuous function on $(0,+\infty)$ which
may have a singularity at zero.
Bennewitz
,
Björn
We show that a result of Lewis and Vogel on uniqueness in a free boundary
problem for the $p$-Laplace operator is sharp in two dimensions.
Junca
,
Stéphane
We study the propagation of high frequency oscillations for one dimensional
semi-linear hyperbolic systems with small parabolic perturbations.
We obtain a new degenerate parabolic system for the profile,
and valid an asymptotic development in the spirit of Joly, Métivier and Rauch.
Chen
,
Yanping; Ding
,
Yong
In this paper the authors prove the $L^2(\mathbb{R}^n)$ boundedness of the
commutator of the singular integral operator with rough variable
kernels, which is a substantial improvement and extension of some known results.
Schuster
,
Alexander; Varolin
,
Dror
We find sufficient conditions for a discrete sequence to be
interpolating or sampling for certain generalized Bergman spaces on
open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerdá,
Seip, Wallsten and others, our conditions for interpolation
and sampling are as follows: If a certain upper density of the
sequence has value less that 1, then the sequence is interpolating,
while if a certain lower density has value greater than 1, then the
sequence is sampling.
Unlike previous works, we introduce a family of densities all of
which provide sufficient conditions. Thus we obtain new results even
in classical cases, some of which might be useful in industrial
applications.
The main point...
Germain
,
Pierre
We consider the critical semilinear wave equation
\begin{equation*}
(NLW)_{2^*-1} \;\;\;
\left\{
\begin{aligned}
\square u + |u|^{2^*-2} u & = 0 \\
u_{|t=0} & = u_0 \\
\partial_t u_{|t=0} & = u_1 \, \,,
\end{aligned} \right.
\end{equation*}
set in $\mathbb{R}^d$, $d \geq 3$, with $2^* = \frac{2d}{d-2} \,\cdotp$ Shatah and
Struwe [Shatah, J. and Struwe, M.: Geometric wave equations. Courant Lecture Notes
in Mathematics 2. New York University, Courant Institute of Mathematical Sciences.
American Mathematical Society, RI, 1998] proved that, for finite energy initial
data (ie if $(u_0,u_1) \in \dot{H}^1 \times L^2$), there exists a global
solution such that $(u,\partial_t u)\in \mathcal{C}(\mathbb{R},\dot{H}^1 \times L^2)$.
Planchon [Planchon, F.: Self-similar solutions and semi-linear wave equations in Besov
spaces. J. Math....
Gállego
,
M. Pilar; Hauck
,
Peter; Pérez-Ramos
,
M. Dolores
The main result in the paper states the following: For a finite
group $G=AB$, which is the product of the soluble subgroups $A$
and $B$, if $\langle a,b \rangle$ is a metanilpotent group for all
$a\in A$ and $b\in B$, then the factor groups $\langle a,b \rangle
F(G)/F(G)$ are nilpotent, $F(G)$ denoting the Fitting subgroup of
$G$. A particular generalization of this result and some
consequences are also obtained. For instance, such a group $G$ is
proved to be soluble of nilpotent length at most $l+1$, assuming
that the factors $A$ and $B$ have nilpotent length at most $l$. Also
for any finite soluble group $G$ and $k\geq 1$,...
Desvillettes
,
Laurent; Fellner
,
Klemens
In the continuation of [Desvillettes, L., Fellner, K.:
Exponential Decay toward Equilibrium via Entropy Methods for Reaction-Diffusion Equations.
J. Math. Anal. Appl. 319 (2006), no. 1, 157-176], we study reversible reaction-diffusion
equations via entropy methods (based on the free energy functional)
for a 1D system of four species. We improve the existing theory by getting
1) almost exponential convergence in $L^1$ to the
steady state via a precise entropy-entropy
dissipation estimate, 2) an explicit global $L^{\infty}$ bound via interpolation
of a polynomially growing $H^1$ bound with the almost exponential $L^1$ convergence,
and 3), finally, explicit exponential convergence to the steady state in all
Sobolev norms.
Bujalance
,
Emilio; Cirre
,
Francisco Javier; Gamboa
,
José Manuel; Gromadzki
,
Grzegorz
Let $X$ be a symmetric compact Riemann surface whose full group of
conformal automorphisms is cyclic. We derive a formula for counting
the number of ovals of the symmetries of $X$ in terms of few data of
the monodromy of the covering $X\rightarrow X/G$, where
$G=\mbox{\rm Aut\/}^\pm X$ is the full group of conformal and
anticonformal automorphisms of $X$.
Andreu , Fuensanta; Caselles , Vicent; Mazón , José Manuel
We give the correct proof of Lemma 3.6 of the paper {\it A Parabolic Quasilinear
Problem for Linear Growth Functionals} (Rev. Mat. Iberoamericana {\bf 18}
(2002), no. 1, 135-185).
Massaneda , Xavier; Thomas , Pascal J.
We propose a definition of sampling set for the Nevanlinna and Smirnov classes
in the disk and show its equivalence with the notion of determination set for
the same classes. We also show the relationship with determination sets for
related classes of functions and deduce a characterization of Smirnov sampling
sets. For Nevanlinna sampling we give general conditions (necessary or
sufficient), from which we obtain precise geometric descriptions in several
regular cases.
Bonheure , Denis; Van Schaftingen , Jean
We deal with the existence of positive bound state solutions for a class of
stationary nonlinear Schr�dinger equations of the form $$ -\varepsilon^2\Delta u
+ V(x) u = K(x) u^p,\qquad x\in\mathbb{R}^N, $ where $V, K$ are positive
continuous functions and $p > 1$ is subcritical, in a framework which may
exclude the existence of ground states. Namely, the potential $V$ is allowed to
vanish at infinity and the competing function $K$ does not have to be bounded.
In the \emph{semi-classical limit}, i.e. for $\varepsilon\sim 0$, we prove the
existence of bound state solutions localized around local minimum points of the
auxiliary function $\mathcal{A} = V^\theta K^{-\frac{2}{p-1}}$, where
$\theta=(p+1)/(p-1)-N/2$. A...
Deng , Donggao; Duong , Xuan Thinh; Sikora , Adam; Yan , Lixin
Let $L$ be a generator of a semigroup satisfying the Gaussian upper bounds. A
new ${\rm BMO}_L$ space associated with $L$ was recently introduced in [Duong,
X. T. and Yan, L.: {New function spaces of BMO type, the John-Nirenberg
inequality, interpolation and applications}. \textit{Comm. Pure Appl. Math.}
{\bf 58} (2005), 1375-1420] and [Duong, X. T. and Yan, L.: {Duality of Hardy and
BMO spaces associated with operators with heat kernels bounds}. \textit{J. Amer.
Math. Soc.} {\bf 18} (2005), 943-973]. We discuss applications of the new ${\rm
BMO}_L$ spaces in the theory of singular integration. For example we obtain
${\rm BMO}_L$ estimates and interpolation results for fractional powers, purely
imaginary...
Krötz , Bernhard; Thangavelu , Sundaram; Xu , Yuan
We study the heat kernel transform on a nilmanifold $M$ of the Heisenberg group.
We show that the image of $L^2(M)$ under this transform is a direct sum of
weighted Bergman spaces which are related to twisted Bergman and Hermite-Bergman
spaces.
Villamayor U. , Orlando
Let $V$ be a smooth scheme over a field $k$, and let $\{I_n, n\geq 0\}$ be a
filtration of sheaves of ideals in $\mathcal{O}_V$, such that
$I_0=\mathcal{O}_V$, and $I_s\cdot I_t\subset I_{s+t}$. In such case $\bigoplus
I_n$ is called a Rees algebra. A Rees algebra is said to be a differential
algebra if, for any two integers $N > n$ and any differential operator
$D$ of order $n$, $D(I_N)\subset I_{N-n}$. Any Rees algebra extends to a
smallest differential algebra. There are two extensions of Rees algebras of
interest in singularity theory: one defined by taking integral closures, and
another by extending the algebra to a differential algebra. We study...