Recursos de colección
Cerveau, D.; Garba Belko, D.; Meziani, R.
We relate some properties of complexifications of real analytic foliations with problems such that existence of first integrals or convergent normalizations. Holomorphic diffeomorphisms having an invariant real foliation play a crucial role.
Aramayona, Javier; Haïssinsky, Peter
We show that an injective continuous map between planar regions which distorts vertices of equilateral triangles by a small amount is quasiconformal.
Deschamps, Guillaume
In this article we use the twistor theory in order to build ``non standard'' complex structures (with a meaning which we define) on the products of $4$-manifolds with the sphere of dimension two. To that end, we enumerate the set of complex surfaces whose twistor space is $\mathcal C^\infty$-trivial. Among these surface we will study those which admit an anti-self-dual riemannian metric.
Carrillo, J. A.; Gualdani, M. P.; Jüngel, A.
A nonlinear degenerate Fokker-Planck equation in the whole space is analyzed. The existence of solutions to the corresponding implicit Euler scheme is proved, and it is shown that the semi-discrete solution converges to a solution of the continuous problem. Furthermore, the discrete entropy decays monotonically in time and the solution to the continuous problem is unique. The nonlinearity is assumed to be of porous-medium type. For the (given) potential, either a less than quadratic growth condition at infinity is supposed or the initial datum is assumed to be compactly supported. The existence proof is based on regularization and maximum principle...
Mercaldo, A.; Segura de León, S.; Trombetti, C.
In the present paper we study the behaviour as $p$ goes to$1$ of the weak solutions to the problems
$$ \begin{cases}-\operatorname{div} \bigl(|\nabla u_p|^{p-2}\nabla u_p\bigr)=f \text{in } \Omega\\ u_p=0 \text{on } \partial\Omega, \end{cases}$$
¶ where $\Omega$ is a bounded open set of ${\mathbb R}^N$ $(N\ge 2)$ with Lipschitz boundary and $p>1$. As far as the datum $f$ is concerned, we analyze several cases: the most general one is $f\in W^{-1,\infty}(\Omega)$. We also illustrate our results by means of remarks and examples.
Jarboui, Noômen; Jerbi, Ayada
This paper deals with the universal catenarity of a pullback construction ring. It seeks necessary and sufficient conditions for such a pullback to have the universal catenarity, improving some known results. Its main result leads to new examples of universally catenarian domains.
Harjulehto, Petteri; Hästö, Peter
We study Sobolev embeddings in the Sobolev space $W^{1,p(\cdot)}(\Omega)$ with variable exponent satisfying $1\leqslant p(x) \leqslant n$. Since the exponent is allowed to reach the values $1$ and $n$, we need to introduce new techniques, combining weak- and strong-type estimates, and a new variable exponent target space scale which features a space of exponential type integrability instead of $L^\infty$ at the upper end.
Elduque, Alberto; Okubo, Susumu
The classical Tits construction provides models of the exceptionalsimple Lie algebras in terms of a unital composition algebra and a degree three simple Jordan algebra. A couple of actions of the symmetric group $S_4$ on this construction are given. By means of these actions, the models provided by the Tits construction are related to models of the exceptional Lie algebras obtained from two different types of structurable algebras. Some models of exceptional Lie superalgebras are discussed too.
Melnikov, Mark; Poltoratski, Alexei; Volberg, Alexander
If $\mu$ is a finite complex measure in the complex plane $\mathbb{C}$ we denote by $C^\mu$ its Cauchy integral defined in the sense of principal value. The measure $\mu$ is called reflectionless if it is continuous (has no atoms) and $C^\mu=0$ at $\mu$-almost every point. We show that if $\mu$ is reflectionless and its Cauchy maximal function $C^\mu_*$ is summable with respect to $|\mu|$ then $\mu$ is trivial. An example of a reflectionless measure whose maximal function belongs to the ``weak" $L^1$ is also constructed, proving that the above result is sharp in its scale. We also give a partial...
Salomone, Stephanie Anne
The following deals with the $T(b)$ theorems of David, Journé, and Semmes considered in a dyadic setting. We find sharp growth estimates for a global and a local dyadic $T(b)$ Theorem. We use multiscale analysis and Haar wavelets in the local case.
Constantin, Peter
We present results concerning the local existence, regularity and possible blow up of solutions to incompressible Euler and Navier-Stokes equations.
Otway, Thomas H.
Energy inequalities are derived for an elliptic-hyperbolic operator arising in plasma
physics. These inequalities imply the existence of distribution and weak solutions to
various closed boundary-value problems. An existence theorem is proven for a related
class of Keldysh equations, and the failure of expected methods for obtaining uniqueness
is discussed. The proofs use ideas recently introduced by Lupo, Morawetz, and Payne for
a generalized Tricomi operator. The existence of strong solutions under open boundary
conditions is also proven.
Brochero Martínez, F. E.; Cano, F.; López-Hernanz, L.
We give a simple proof of the existence of parabolic curves for diffeomorphisms in
$(\mathbb{C}^2,{0})$ tangent to the identity with isolated fixed point.
Globevnik, Josip
Let $\Delta $ be the open unit disc in $\mathbb{C}$. Given a continuous function
$\varphi \colon b\Delta \rightarrow \mathbb{C}\setminus \{ 0\}$ denote by $\mathcal{W}
(\varphi )$ the winding number of $\varphi$ around the origin. We prove that a
continuous function $f\colon b\Delta\rightarrow \mathbb{C}$ extends meromorphically
through $\Delta $ if and only if there is a number $N\in \mathbb{N}\cup\{ 0\}$ such that
$\mathcal{W} (Pf+Q)\geq -N$ for every pair $P$, $Q$ of polynomials such that $Pf+Q\not=
0$ on $b\Delta$. If this is the case then the meromorphic extension has at most $N$
poles in $\Delta$.
Kurdachenko, Leonid A.; Muñoz-Escolano, José M.; Otal, Javier
Let $V$ be a vector space over a field $F$. If $G\!\leq\! GL(V,F)$, the central
dimension of $G$ is the $F$-dimension of the vector space $V/C_V(G)$. In [DEK] and
[KS], soluble linear groups in which the set $\mathcal{L}_{\operatorname{icd}}(G)$ of
all proper infinite central dimensional subgroups of $G$ satisfies the minimal condition
and the maximal condition, respectively, have been described. On the other hand, in
[MOS], periodic locally radical linear groups in which
$\mathcal{L}_{\operatorname{icd}}(G)$ satisfies one of the weak chain conditions (the
weak minimal condition or the weak maximal condition) have been characterized. In this
paper, we begin the study of the non-periodic case by describing locally nilpotent
linear groups...
Perera, Francesc; Siles Molina, Mercedes
In this paper we examine how the notion of algebra of quotients for Lie algebras ties
up with the corresponding well-known concept in the associative case. Specifically, we
completely characterize when a Lie algebra $Q$ is an algebra of quotients of a Lie
algebra $L$ in terms of the associative algebras generated by the adjoint operators of
$L$ and $Q$ respectively. In a converse direction, we also provide with new examples of
algebras of quotients of Lie algebras and these come from associative algebras of
quotients. In the course of our analysis, we make use of the notions of density and
multiplicative semiprimeness to link our results...
Bernardis, A. L.; Martín-Reyes, F. J.
In this paper we obtain convergence results for the series of differences of Cesàro
averages along lacunary sequences in the setting of weighted $L^p$-spaces. These results
give some information about how the Cesàro averages converge. The paper extends results
of an earlier work by R. L. Jones and J. Rosenblatt. The operators considered are
essentially convolution operators given by kernels more singular than the ones in the
article by Jones and Rosenblatt.
Hencl, Stanislav
Let $\Omega\subset\mathbb{R}^n$ be open and suppose that $f\colon
\Omega\to\mathbb{R}^n$ is a bilipschitz mapping such that $Df\in
BV_{\operatorname{loc}}(\Omega,\mathbb{R}^{n^2})$. We show that under these assumptions
the inverse satisfies $Df^{-1}\in
BV_{\operatorname{loc}}(f(\Omega),\mathbb{R}^{n^2})$.
Brady, Tom; Burillo, José; Cleary, Sean; Stein, Melanie
We describe some properties of braided generalizations of Thompson's groups, introduced
by Brin and Dehornoy. We give slightly different characterizations of the braided
Thompson's groups $BV$ and $\widehat{BV}$ which lead to natural presentations which
emphasize one of their subgroup-containment properties. We consider pure braided
versions of Thompson's group $F$. These groups, $BF$ and $\widehat{BF}$, are subgroups
of the braided versions of Thompson's group $V$. Unlike $V$, elements of $F$ are
order-preserving self-maps of the interval and we use pure braids together with elements
of $F$ thus again preserving order. We define these pure braided groups, give normal
forms for elements, and construct infinite and finite presentations of these...
Agrafeuil , Cyril; Zarrabi, Mohamed
We denote by $\mathbb{T}$ the unit circle and by $\mathbb{D}$ the unit disc. Let
$\mathcal{B}$ be a semi-simple unital commutative Banach algebra of functions
holomorphic in $\mathbb{D}$ and continuous on $\overline{\mathbb{D}}$, endowed with the
pointwise product. We assume that $\mathcal{B}$ is continously imbedded in the disc
algebra and satisfies the following conditions:
¶ The space of polynomials is a dense subset of $\mathcal{B}$.
¶ $\lim_{n\to +\infty}\|z^n\|_{\mathcal{B}}^{1/ n}=1$.
¶ There exist $k \geq 0$ and $C > 0$ such that $$ \bigl| 1- |\lambda| \bigr|^{k}
\bigl\| f \bigr\|_{\mathcal{B}} \leq C \bigl\| (z-\lambda) f \bigr\|_{\mathcal{B}},
\quad (f \in \mathcal{B},\, |\lambda| < 2).$$
¶ When $\mathcal{B}$ satisfies in addition the analytic Ditkin condition,...