Sumario:
Revista Matemática Complutense
Servicio de Publicaciones de la Universidad Complutense de Madrid
Vol 22 Nº 1 (2009)
Más información/Texto completo en http://revistas.ucm.es/portal/ ....

Contenidos  Contents 4 Uniqueness of Entropy Solutions of Nonlinear EllipticParabolicHyperbolic Problems in One Dimension Space OUARO, Stanislas 7
Palabras Clave: Elliptic; Parabolic; Hyperbolic; Weak solution; Entropy solution; L1contraction Resumen: We consider a class of ellipticparabolichyperbolic degenerate equations of the form b(u)t — a(u, φ(ux)x= f with homogeneous Dirichlet conditions and initial conditions. In this paper we prove an L1contraction principle and the uniqueness of entropy solutions under rather general assumptions on the data.
Renormalized Solutions for Nonlinear Degenerate Elliptic Problems with L1 Data AMMAR, Kaouther  REDWANE, Hicham 37
Palabras Clave: Renormalized solutions; Nonlinear degenerate elliptic equations; Weighted Sobolev spaces Resumen: We are interested in a class of nonlinear degenerate diffusion problems with a diffusion function a(x, u, Vu) which is not controlled with respect to u and which is not uniformly coercive on the weighted Sobolev spaces W1,p0 (Ω, w). Existence of a renormalized solution is proved in the L1setting.
Semistability of Certain Bundles on a Quintic CalabiYau Threefold BRAMBILLA, Maria Chiara 53
Palabras Clave: Semistability; Vector bundles Resumen: In a recent paper Douglas and Zhou aim for explicit examples of string theory compactifications that have a different number of generations and can be connected. For this purpose, they provide a list of bundles on a quintic CalabiYau threefold. They need to show that (at least some of) these bundles are semistable and leave this as an open question. In this paper we prove the semistability of most of the bundles in the list, thus completing the result of Douglas and Zhou.
Solving Variational Inclusions by a Method Obtained Using a Multipoint Iteration Formula CABUZEL, Catherine  PIETRUS, Alain 63
Palabras Clave: Setvalued mapping; Generalized equations; PseudoLipschitz maps; Multipoint iteration formula Resumen: This paper deals with variational inclusions of the form: 0 ε f(x)+F(x) where f is a single function admitting a second order Fréchet derivative and F is a setvalued map acting in Banach spaces. We prove the existence of a sequence (xk) satisfying 0 ε f(xk)+∑M i=1 aiΛf(xk+βi(xk+1xk))(xk+1xk)+F(xk+1) where the singlevalued function involved in this relation is an approximation of the function f based on a multipoint iteration formula and we show that this method is locally cubically convergent.
A Discrete HardyLaptevWeidlType Inequality and Associated SchrödingerType Operators EVANS, W. Desmond  SCHMIDT, Karl Michael 75
Palabras Clave: Discrete Schrödinger operator; AharonovBohm magnetic potential Resumen: Although the classical Hardy inequality is valid only in the three and higher dimensional case, Laptev and Weidl established a twodimensional Hardytype inequality for the magnetic gradient with an AharonovBohm magnetic potential. Here we consider a discrete analogue, replacing the punctured plane with a radially exponential lattice. In addition to discrete Hardy and Sobolev inequalities, we study the spectral properties of two associated selfadjoint operators. In particular, it is shown that, for suitable potentials, the discrete Schrödingertype operator in the AharonovBohm field has essential spectrum concentrated at 0, and the multiplicity of its lower spectrum satisfies a CLRtype inequality.
Existence of Renormalized Solution of Some Elliptic Problems in Orlicz Spaces AHAROUCH, Lahsen  BENNOUNA, Jaouad  TOUZANI, Abdelfettah 91
Palabras Clave: Orlicz Sobolev spaces; Boundary value problems; Truncations; Renormalized Resumen: In this paper, we study the problem:—div a(x, u, ∆u) — div Φ(u) + g(x; u) = f in the framework of Orlicz spaces. The main contribution of our work is to prove the existence of a renormalized solution without any restriction on the Nfunction of the Orlicz space.
On Dilation Operators in Besov Spaces SCHNEIDER, Cornelia 111
Palabras Clave: Besov spaces; Dilation operators; Moment conditions Resumen: We consider dilation operators Tk : f → f(2k.) in the framework of Besov spaces Bsp,q (Rn) when 0 < p≤ 1. If s > n(1/p — 1) Tk is a bounded linear operator from Bsp,q (Rn) into itself and there are optimal bounds for its norm. We study the situation on the line s = n(1/p — 1), an open problem mentioned in [5, 2.3.1, 2.3.2]. It turns out that the results shed new light upon the diversity of different approaches to Besov spaces on this line, associated to definitions by differences, Fourieranalytical methods, and subatomic decompositions.
Newton Binomial Formulas in Schubert Calculus CORDOVEZ, Jorge  GATTO, Letterio  SANTIAGO, Taíse 129
Palabras Clave: Schubert Calculus on a Grassmann algebra; Newton’s binomial formulas in Schubert calculus; Enumerative geometry of linear series on the projective line Resumen: We prove Newton’s binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.
Extremal Vector Valued Inequalities for Hankel Transforms ROMERA, Elena 153
Palabras Clave: Disc multiplier; FourierHankel transforms Boundary Sentinels with Given Sensitivity MASSENGO MOPHOU, Gisèle  PUEL, Jeanpierre 165
Palabras Clave: Heat equation; Optimal control; Controllability; Carleman inequalities; Sentinels Resumen: The notion of sentinels with given sensitivity was introduced by J.L. Lions in [10] in order to identify parameters in a problem of pollution ruled by a semilinear parabolic equation. He proves that the existence of such sentinels is reduced to the solution of exact controllability problem with constraints on the state. Reconsidering this notion of sentinels in a more general framework, we prove the existence of the new sentinels by solving a boundary nullcontrollability problem with constraint on the control. Our results use a Carleman inequality which is adapted to the constraint.
A Symbolic Calculus and a Parametrix Construction for Pseudodifferential Operators with NonSmooth Negative Definite Symbols POTRYKUS, Alexander 187
Palabras Clave: Symbolic calculus; Nonsmooth symbols; Negative definite functions; Feller semigroups Resumen: We consider pseudodifferential operators that have nonsmooth negative definite symbols and develop a corresponding symbolic calculus. Combining this symbolic calculus with the use of nonsmooth symbols that are asymptotically constant in the covariable we succeed infunding a parametrix for a certain pseudodifferential equation. This in turn allows us to show that some pseudodifferential operators with nonsmooth negative definite symbols are pregenerators of Feller semigroups.
About the Banach Envelope of l1,∞ PIETSCH, Albrecht 209
Palabras Clave: Banach envelope; Marcinkiewicz space l1,∞; Weak l1space Resumen: We study the Banach envelope of the quasiBanach space l1,∞ consisting of all sequences x=(ξ k) with sn(x)=O(1/n), where (sn (x)) denotes the nonincreasing rearrangement of x=(ξ k) The situation turns out to be much more complicated than that in the wellknown case of the separable subspace lo1,∞, whose members are characterized by sn(x) =o(1/n).
2Microlocal Besov and TriebelLizorkin Spaces of Variable Integrability KEMPKA, Henning 227
Palabras Clave: Besov spaces; TriebelLizorkin spaces; 2microlocal spaces; Variable smoothness; Variable integrability; Local means Resumen: We introduce 2microlocal Besov and TriebelLizorkin spaces with variable integrability and give a characterization by local means. These spaces cover spaces of variable exponent, spaces of variable smoothness and weighted spaces that have been studied in recent years.
Besov and TriebelLizorkin Spaces Related to Singular Integrals with Flag Kernels YANG, Dachun 253
Palabras Clave: Besov space; TriebelLizorkin space; Flag singular integral; Flag fractional integral; LittlewoodPaley operator; Dual space; Lifting; Embedding Resumen: Let s1, s2 Є (—1, 1) and s = (s1, s2). In this paper, the author introduces the Besov space Bspqq(R2) with p, q Є [1, ∞] and the TriebelLizorkin space Fspqq(R2) with p Є (1, ∞) and q Є (1, ∞] associated to singular integrals with flag kernels. Some basic properties, including their dual spaces, some equivalent norm characterizations via LittlewoodPaley functions, lifting properties and some embedding theorems, on these spaces are given. Moreover, the au thor obtains the boundedness of flag singular integrals and fractional integrals on these spaces.
Erratum to “Feller Semigroups Obtained by Variable Order Subordination" (Rev. Mat. Complut. 20 (2007), no. 2, 293307) EVANS, Kristian P.  JACOB, Niels 303
