Showing papers in "Revista Matematica Complutense in 2009"
TL;DR: In this article, an overview of known and new results about the coupling of Navier-Stokes and Darcy equations to model the filtration of incompressible fluids through porous media is presented.
Abstract: This paper is an overview of known and new results about the coupling of Navier-Stokes and Darcy equations to model the filtration of incompressible fluids through porous media. We discuss coupling conditions and we analyze the global coupled model in order to prove its well-posedness and to characterize effective algorithms to compute the solution of its numerical approximation.
209 citations
TL;DR: In this article, the authors introduce 2-microlocal Besov and Triebel-Lizorkin spaces with variable integrability and give a characterization by local means.
Abstract: We introduce 2-microlocal Besov and Triebel-Lizorkin 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.
87 citations
TL;DR: In this paper, the fundamental group of the complement of the torus knot of type (m, n) is defined and a geometric description of the character variety X(G) of characters of representations of G into SL(2,C).
Abstract: Let G be the fundamental group of the complement of the torus knot of type (m, n). This has a presentation G = ‹x, y | xm= yⁿ›. We find the geometric description of the character variety X(G) of characters of representations of G into SL(2,C).
38 citations
TL;DR: In this paper, the Banach envelope of the quasi-Banach space l 1,8 consisting of all sequences x=(E k) with sn(x) = O(1/n), where (sn (x)) denotes the non-increasing rearrangement of x = E k.
Abstract: We study the Banach envelope of the quasi-Banach space l1,8 consisting of all sequences x=(E k) with sn(x)=O(1/n), where (sn (x)) denotes the non-increasing rearrangement of x=(E k) The situation turns out to be much more complicated than that in the well-known case of the separable subspace lo1,8, whose members are characterized by sn(x) =o(1/n).
23 citations
TL;DR: In this paper, the authors considered the problem of finding the optimal norm of a bounded linear operator on the line s = n(1/p − 1) where s is the number of points in the plane.
Abstract: We consider dilation operators T k : f → f(2 k .) in the framework of Besov spaces B s p,q (R n ) when 0 n(1/p — 1) Tk is a bounded linear operator from B s p,q (R n ) 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, Fourier-analytical methods, and subatomic decompositions.
23 citations
TL;DR: The main contribution of as mentioned in this paper is to prove the existence of a renormalized solution without any restriction on the N-function of the Orlicz space, which is the case in this paper.
Abstract: 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 N-function of the Orlicz space.
23 citations
TL;DR: In this article, the authors characterize boundedness and compactness of weighted composition operators acting between Dirichlet type spaces by using Carleson measures and find essential norm estimates for these operators.
Abstract: In this work we characterize boundedness and compactness of weighted composition operators acting between Dirichlet type spaces by using Carleson measures. We also find essential norm estimates for these operators.
16 citations
TL;DR: In this article, the existence of sentinels with given sensitivity was proved by solving a boundary null-controllability problem with constraint on the control, using a Carleman inequality adapted to the constraint.
Abstract: 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 null-controllability problem with constraint on the control. Our results use a Carleman inequality which is adapted to the constraint.
12 citations
TL;DR: In this article, Newton's binomial formulas for Schubert Calculus were used to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.
Abstract: 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.
12 citations
TL;DR: In this article, the authors derive sharp Sobolev inequalities for H¨ormander vector fields and obtain new sharp embedding embeddings and Faber-Krahn estimates.
Abstract: We derive sharp Sobolev inequalities for Sobolev spaces on metric spaces. In particular, we obtain new sharp Sobolev embeddings and Faber-Krahn estimates for H¨ormander vector fields.
11 citations
TL;DR: In this paper, the semistability of most of the bundles in the Calabi-Yau list has been proved, thus completing the result of Douglas and Zhou, who showed that most of these bundles are semistable.
Abstract: 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 Calabi-Yau 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.
TL;DR: In this paper, the authors introduced the triebel-lizorkin space and the Besov space for singular integrals with flag kernels and obtained the boundedness of fractional integrals on these spaces.
Abstract: Let s 1 , s 2 Є (—1, 1) and s = (s 1 , s 2 ). In this paper, the author introduces the Besov space B s pq q(R 2 ) with p, q Є [1, ∞] and the Triebel-Lizorkin space F s pq q(R 2 ) 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 Littlewood-Paley 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.
TL;DR: In this paper, it was shown that the Taylor series is universal with respect to overconvergence if and only if its Cesaro (C, k)-means are universal for any real k > −1.
Abstract: Let Ω a domain in the complex plane such that Ω satisfies appropriate geometrical and topological properties. We prove that if f is a holomorphic function in Ω, then its Taylor series, with center at any ξ Є Ω , is universal with respect to overconvergence if and only if its Cesaro (C, k)-means are universal for any real k > −1. This is an extension of the same result, proved recently by F. Bayart, for any integer k ≥ 0. As a consequence, several classes of universal functions introduced in the related literature are shown to coincide.
TL;DR: Lower and upper bounds for the Kottman separation constant of Orlicz sequence spaces equipped with the Luxemburg norm are given in this paper, involving moduli of asymptotic uniform convexity and smoothness.
Abstract: We give lower and upper bounds, involving moduli of asymptotic uniform convexity and smoothness, for the Kottman separation constant of Orlicz sequence spaces equipped with the Luxemburg norm.
TL;DR: In this paper, a variational inclusions of the form: 0 e f(x)+F(x) where f is a single function admitting a second order Frechet derivative and F is a set-valued map acting in Banach spaces was studied.
Abstract: This paper deals with variational inclusions of the form: 0 e f(x)+F(x) where f is a single function admitting a second order Frechet derivative and F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (x k ) satisfying 0 e f(x k )+∑ M i=1 a i Λf(x k +β i (x k+1 -x k ))(x k+1 -x k )+F(x k+1 ) where the single-valued 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.
TL;DR: In this paper, the uniqueness of entropy solutions for a class of elliptic-parabolic-hyperbolic degenerate equations with homogeneous Dirichlet conditions and initial conditions was proved.
Abstract: We consider a class of elliptic-parabolic-hyperbolic degenerate equations of the form b(u)t -a(u, f(ux)x= f with homogeneous Dirichlet conditions and initial conditions. In this paper we prove an L1-contraction principle and the uniqueness of entropy solutions under rather general assumptions on the data.
TL;DR: In this article, the authors consider pseudodifferential operators with non-smooth 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 co-variable.
Abstract: We consider pseudodifferential operators that have non-smooth negative definite symbols and develop a corresponding symbolic calculus. Combining this symbolic calculus with the use of non-smooth symbols that are asymptotically constant in the co-variable we succeed infunding a parametrix for a certain pseudodifferential equation. This in turn allows us to show that some pseudodifferential operators with non-smooth negative definite symbols are pregenerators of Feller semigroups.
TL;DR: In this article, a Varchenko type formula for a one-parameter deformation of an analytic complex function is given for the case where the deformation is non-degenerate with respect to its Newton diagram.
Abstract: For a one-parameter deformation of an analytic complex function germ of several variables, there is defined its monodromy zeta-function. We give a Varchenko type formula for this zeta-function if the deformation is non-degenerate with respect to its Newton diagram.
TL;DR: In this article, the fundamental groups of some special quadric arrangements are extended with a new Corollary 2.10, which does not appear in the original paper, and the original Theorems 2.2, 2.4 and 2.7 are extended.
Abstract: This erratum relates to our work “Fundamental groups of some special quadric arrangements”. The original Theorems 2.2, 2.5, 2.8 and Propositions 2.3(ii)(iii), 2.6(ii)(iii), 2.9(ii)(iii) have wrong results. They need to be rephrased. Corollaries 2.4 and 2.7 are incomplete, and they are extended. We add a new Corollary 2.10, which does not appear in the original paper. Proposition 3.1 has a wrong result and it is rephrased and reproved. In Proposition 4.1 and its Corollary 4.2 a slight error has occurred: as the correct proofs in the paper show, the monodromy is a quadruple fulltwist.
TL;DR: In this paper, 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 uniformly coercive on the weighted Sobolev spaces W1,p0 (O, w).
Abstract: 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 (O, w). Existence of a renormalized solution is proved in the L1-setting.
TL;DR: In this article, it was shown that the disc multiplier is bounded on the spaces L pq (r n−1 dr) when 2n n+1
Abstract: The disc multiplier may be seen as a vector valued operator when we consider its projections in terms of the spherical harmonics. In this form, it represents a vector valued Hankel transform. We know that, for radial functions, it is bounded on the spaces L pq (r n−1 dr) when 2n n+1
TL;DR: In this paper, it was shown that for suitable potentials, the discrete Schrodinger-type operator has essential spectrum concentrated at 0, and the multiplicity of its lower spectrum satisfies a CLR-type inequality.
Abstract: Although the classical Hardy inequality is valid only in the three- and higher dimensional case, Laptev and Weidl established a two-dimensional Hardy-type inequality for the magnetic gradient with an Aharonov-Bohm 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 self-adjoint operators. In particular, it is shown that, for suitable potentials, the discrete Schrodingertype operator in the Aharonov-Bohm field has essential spectrum concentrated at 0, and the multiplicity of its lower spectrum satisfies a CLR-type inequality.