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JournalISSN: 1139-1138

Revista Matematica Complutense 

Springer Science+Business Media
About: Revista Matematica Complutense is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Banach space & Bounded function. It has an ISSN identifier of 1139-1138. Over the lifetime, 901 publications have been published receiving 10819 citations.


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Journal ArticleDOI
TL;DR: In this article, the authors present a survey of recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension and present some of the latest results on uniqueness and stability of entropy weak solutions.
Abstract: This is a survey paper, written in the occasion of an invited talk given by the author at the Universidad Complutense in Madrid, October 1998. Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak solutions.

964 citations

Journal ArticleDOI
TL;DR: In this article, a generalization of Hardy's and Poincaré's inequalities is proposed to deal with unbaunded exiremal solution problems in a continuous, positive, increasing and convex funetion setting.
Abstract: posed in a baunded domain fi of R~ with smooth boundary 8 SI wiih Dirichiel dala u100 = O, and a continuous, positive, increasing and convex funetion f an [O,oc) such thai f(s)/s — 00 as a —. oc>. Under Ihese conditions Ihere is a maximal or extremal value of the parameter A > O such thaI ihe problem has a solution. We invesligate Ihe exisience and properties of Ihe corresponding extrema) solutions when Ihe>’ are unhaunded (i.e., singular or blow-up solutions). We characterize ihe singular Hí extremal solulions and ihe extrenial value by a eriterioncansisiing of twa condiiions: (i) they musí be ener~’ saluiions, mal in L~; (Ii) tite>’ musí sntisfy a Hardy inequalil>’ which transíates Ihe fact thai ihe firsí eigenvalue of the linearized aperator is nannegalive. In arder to apply ibis characlerizatiat to ihe typical examples arising in Ihe lilerature we need an improved version of ihe cíassical Hardy inequalil>’ wiih besí constaní. We aiablish such a resulí as a simultaneous generalization of Hardy’s and Poincaré’s inequaUiies for ah dirnensions n > 2. A striking prapert>’ of sorne examples of unbaunded exiremal solutiona is the fact thai tite hinearization of ihe prablem araund them happens to be formalí>’ invertible and nevertheless tite npplication of ihe Inverse and Imphicii Funetion iheorems falís to produce Ihe usual exislence ar continuation resulís. We consider ihis question and explain tite pitenomenon as a lack of appropriate funetional setting.

631 citations

Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: In this paper, the authors deal with function spaces of Bs pq and F s pq type in Lipschitz domains and on Lipschnitz manifolds in a systematic (although not comprehensive) way.
Abstract: Function spaces of type Bs pq and Fs pq cover as special cases classical and fractional Sobolev spaces, classical Besov spaces, Holder- zgmund spaces and inhomogeneous Hardy spaces. In the last or 3 decades they haven been studied preferably on Rn and in mooth bounded domains in Rn including numerous applications to pseudodi_erential operators, elliptic boundary value problems etc. To a lesser extent spaces of this type have been considered in Lipschitz domains. But in recent times there is a growing interest to study and to use spaces of this type in Lipschitz domains and on their boundaries. It is the aim of this paper to deal with function spaces of Bs pq and Fs pq type in Lipschitz domains and on Lipschitz manifolds in a systematic (although not comprehensive) way: We describe and comment on known results, seal some gaps, give new proofs, and add a few new results of relevant aspects.

199 citations

Journal ArticleDOI
TL;DR: A unified introduction to the dynamics of interval exchange maps and related topics, such as the geometry of translation surfaces, renormalization operators, is given in this paper, where the authors also present a unified analysis of the interval exchange map dynamics.
Abstract: A unified introduction to the dynamics of interval exchange maps and related topics, such as the geometry of translation surfaces, renormalization operators,

186 citations

Performance
Metrics
No. of papers from the Journal in previous years
YearPapers
202312
202226
202172
202040
201936
201832