Mostrando recursos 1 - 20 de 27

  1. Techniques complexes d'étude d'E.D.O.

    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.

  2. A characterisation of plane quasiconformal maps using triangles

    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.

  3. Espaces twistoriels et structures complexes non standards

    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.

  4. Convergence of an Entropic Semi-discretization for Nonlinear Fokker-Planck Equations in ${\mathbb R}^d$

    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...

  5. On the behaviour of the solutions to $p$-Laplacian equations as $p$ goes to $1$

    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.

  6. Pullbacks and Universal Catenarity

    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.

  7. Sobolev inequalities with variable exponent attaining the values $1$ and $n$

    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.

  8. $S_4$-symmetry on the Tits construction of exceptional Lie algebras and superalgebras

    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.

  9. Uniqueness Theorems for Cauchy Integrals

    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...

  10. Sharp growth estimates for dyadic $b$-input $T(b)$ theorems

    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.

  11. Euler and Navier-Stokes Equations

    Constantin, Peter
    We present results concerning the local existence, regularity and possible blow up of solutions to incompressible Euler and Navier-Stokes equations.

  12. Energy inequalities for a model of wave propagation in cold plasma

    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.

  13. Parabolic curves for diffeomorphisms in $\mathbb{C}^2$

    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.

  14. Meromorphic extendibility and the argument principle

    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 $\Delta$.

  15. Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension

    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...

  16. Associative and Lie algebras of quotients

    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...

  17. Differential transforms of Cesàro averages in weighted spaces

    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.

  18. Bilipschitz mappings with derivatives of bounded variation

    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 $Df^{-1}\in BV_{\operatorname{loc}}(f(\Omega),\mathbb{R}^{n^2})$.

  19. Pure braid subgroups of braided Thompson's groups

    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...

  20. Closed ideals with countable hull in algebras of analytic functions smooth up to the boundary

    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,...

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