Global ETD Search

21	Weighted inequalities and properties of operators and embeddings on function spaces / Weighted inequalities and properties of operators and embeddings on function spaces Slavíková, Lenka January 2016 (has links) The present thesis is devoted to the study of various properties of Banach func- tion spaces, with a particular emphasis on applications in the theory of Sobolev spaces and in harmonic analysis. The thesis consists of four papers. In the first one we investigate higher-order embeddings of Sobolev-type spaces built upon rearrangement-invariant Banach function spaces. In particular, we show that optimal higher-order Sobolev embeddings follow from isoperimetric inequal- ities. In the second paper we focus on the question when the above-mentioned Sobolev-type space is a Banach algebra with respect to a pointwise multiplica- tion of functions. An embedding of the Sobolev space into the space of essentially bounded functions is proved to be the answer to this question in several standard as well as nonstandard situations. The third paper is devoted to the problem of validity of the Lebesgue differentiation theorem in the context of rearrangement- invariant Banach function spaces. We provide a necessary and sufficient condition for the validity of this theorem given in terms of concavity of certain functional depending on the norm in question and we find also alternative characterizations expressed in terms of properties of a maximal operator related to the norm. The object of the final paper is the boundedness of the...
22	Analyse dans les espaces métriques mesurés / Topics on calculus in metric measure spaces Han, Bang-Xian 23 June 2015 (has links) Cette thèse traite de plusieurs sujets d'analyse dans les espaces métriques mesurés, en lien avec le transport optimal et des conditions de courbure-dimension. Nous considérons en particulier les équations de continuité dans ces espaces, du point de vue de fonctionnelles continues sur les espaces de Sobolev, et du point de vue de la dualité avec les courbes absolument continues dans l'espace de Wasserstein. Sous une condition de courbure-dimension, mais sans condition de doublement de mesure ou d'inégalité de Poincaré, nous montrons également l'identification des p-gradients faibles. Nous étudions ensuite les espaces de Sobolev sur le produit tordu de l'ensemble des réels et d'un espace métrique mesuré. En particulier, nous montrons la propriété Sobolev-à-Lipschitz sous une certaine condition de courbure-dimension. Enfin, sous une telle condition et dans le cadre d'une théorie non-lisse de Bakry-Emery, nous obtenons une inégalité améliorée de Bochner et proposons une définition du N-tenseur de Ricci. / This thesis concerns in some topics on calculus in metric measure spaces, in connection with optimal transport theory and curvature-dimension conditions. We study the continuity equations on metric measure spaces, in the viewpoint of continuous functionals on Sobolev spaces, and in the viewpoint of the duality with respect to absolutely continuous curves in the Wasserstein space. We study the Sobolev spaces of warped products of a real line and a metric measure space. We prove the 'Pythagoras theorem' for both cartesian products and warped products, and prove Sobolev-to-Lipschitz property for warped products under a certain curvature-dimension condition. We also prove the identification of p-weak gradients under curvature-dimension condition, without the doubling condition or local Poincaré inequality. At last, using the non-smooth Bakry-Emery theory on metric measure spaces, we obtain a Bochner inequality and propose a definition of N-Ricci tensor. Espace métrique mesuré Condition de courbure-Dimension Transport optimal Espace de Sobolev Théorie de Bakry-Emery Tenseur de Ricci Metric measure space Curvature-Dimension condition Optimal transport Sobolev space Bakry-Emery theory Ricci tensor 515
23	Poloha Orliczova prostoru a optimalita / Positioning of Orlicz space and optimality Musil, Vít January 2014 (has links) Given a rearrangement-invariant Banach function space Y (Ω), we consider the problem of the existence of an optimal (largest) domain Or- licz space LA (Ω) satisfying the Sobolev embedding Wm LA (Ω) !Y (Ω). We present a complete solution of this problem within the class of Marcinkiewicz endpoint spaces which covers several important examples.
24	Regularität schwacher Lösungen nichtlinearer elliptischer und parabolischer Systeme partieller Differentialgleichungen mit Entartung Wolf, Jörg 31 May 2002 (has links) In der vorliegenden Arbeit untersuchen wir schwache Lösungen, die zu einem geeigneten Sobolevraum gehören, q-elliptischer und parabolischer Systeme partieller Differentialgleichungen auf deren Regularität für den Fall 1 / In the present work we study the regularity of weak solution to q-elliptic and parabolic systems partial differential equations in appropriate Sobolev spaces in case 1 partielle Differentialgleichungen Systeme nichlinear Entartung elliptisch parabolisch Regularität partielle Hölderstetigkeit Differenzierbarkeit Differenzenmethode kontrolliertes Wachstum natürliches Wachstum Bochnerintegral Evolutionsgleichungen Hilberttransformation Sobolevräume schwache Lösung PDE systems nonlinear degeneration elliptic parabolic regularity partial Hölder continuity differentiability difference method controlled growth natural growth Bochner integral evolution equation Hilbert transform Sobolev space weak solution 510 Mathematik 27 Mathematik SK 540 ddc:510
25	Sampling Inequalities and Applications / Sampling Ungleichungen und Anwendungen Rieger, Christian 28 March 2008 (has links) No description available. 510 Mathematik Mathematics and Computer Science Deterministische Fehlertheorie Sobolev Raum Kernmethoden Radiale Basisfunktion Approximation Reproduzierender Kern-Hilbertraum Regularisierung deterministic error analysis Sobolev space Kernel-based methods Radial Basis Function Approximation reproducing kernel Hilbert space Regularization 31.49 31.76 boundary value problems} EGFJ 990: None of the above
26	Hopf Bifurcation from Infinity in Asymptotically Linear Autonomous Systems with Delay Biglands, Adrian Unknown Date No description available.
27	Chemické a mechanické procesy v synoviálních tekutinách - modelování, analýza, počítačové simulace / Biochemical and mechanical processes in synovial fluid - modeling, analysis and computational simulations Pustějovská, Petra January 2012 (has links) vi Title: Biochemical and mechanical processes in synovial fluid - modeling, mathematical analysis and computational simulations Author: Petra Pustějovská (petra.pustejovska@karlin.mff.cuni.cz) Department: Matematický ústav UK, Univerzita Karlova v Praze Institut für Angewandte Mathematik, Universität Heidelberg Supervisors: prof. RNDr. Josef Málek CSc., DSc. (malek@karlin.mff.cuni.cz) Matematický ústav UK, Univerzita Karlova v Praze, Prof. Dr. Dr. h.c. mult. Willi Jäger (jaeger@iwr.uni-heidelberg.de) Institut für Angewandte Mathematik, Universität Heidelberg Abstract: Synovial fluid is a polymeric liquid which generally behaves as a viscoelastic fluid due to the presence of polysaccharide molecules called hyaluronan. In this thesis, we study the biological and biochemical properties of synovial fluid, its complex rheology and interaction with synovial membrane during filtration process. From the mathematical point of view, we model the synovial fluid as a viscous incompressible fluid for which we develop a novel generalized power-law fluid model wherein the power-law exponent depends on the concentration of the hyaluronan. Such a model is adequate to describe the flows of synovial fluid as long as it is not subjected to instantaneous stimuli. Moreover, we try to find a suitable linear viscoelastic model...
28	Contribution à l'analyse mathématique et à la résolution numérique d'un problème inverse de scattering élasto-acoustique / Contribution to the mathematical analysis and to the numerical solution of an inverse elasto-acoustic scattering problem Estecahandy, Elodie 19 September 2013 (has links) La détermination de la forme d'un obstacle élastique immergé dans un milieu fluide à partir de mesures du champ d'onde diffracté est un problème d'un vif intérêt dans de nombreux domaines tels que le sonar, l'exploration géophysique et l'imagerie médicale. A cause de son caractère non-linéaire et mal posé, ce problème inverse de l'obstacle (IOP) est très difficile à résoudre, particulièrement d'un point de vue numérique. De plus, son étude requiert la compréhension de la théorie du problème de diffraction direct (DP) associé, et la maîtrise des méthodes de résolution correspondantes. Le travail accompli ici se rapporte à l'analyse mathématique et numérique du DP élasto-acoustique et de l'IOP. En particulier, nous avons développé un code de simulation numérique performant pour la propagation des ondes associée à ce type de milieux, basé sur une méthode de type DG qui emploie des éléments finis d'ordre supérieur et des éléments courbes à l'interface afin de mieux représenter l'interaction fluide-structure, et nous l'appliquons à la reconstruction d'objets par la mise en oeuvre d'une méthode de Newton régularisée. / The determination of the shape of an elastic obstacle immersed in water from some measurements of the scattered field is an important problem in many technologies such as sonar, geophysical exploration, and medical imaging. This inverse obstacle problem (IOP) is very difficult to solve, especially from a numerical viewpoint, because of its nonlinear and ill-posed character. Moreover, its investigation requires the understanding of the theory for the associated direct scattering problem (DP), and the mastery of the corresponding numerical solution methods. The work accomplished here pertains to the mathematical and numerical analysis of the elasto-acoustic DP and of the IOP. More specifically, we have developed an efficient numerical simulation code for wave propagation associated to this type of media, based on a DG-type method using higher-order finite elements and curved edges at the interface to better represent the fluid-structure interaction, and we apply it to the reconstruction of objects with the implementation of a regularized Newton method. Interaction fluide-solide Problème de diffraction Fréquence de Jones Inégalité de Gärding Alternative de Fredholm Espace de Sobolev à poids Méthode de Galerkin discontinue Méthode élément fini Raffinement hp Effet de pollution Arêtes de frontière courbes Factorisation LU Différentiabilité au sens de Fréchet Dérivée de domaine Frontière Lipschitzienne Théorème des fonctions implicites Méthode de Newton Régularisation de Tikhonov Domaine étoilé B-splines quadratiques Fluid-solid interaction Scattering problem Jones frequency Gärding's inequality Fredholm alternative Weighted Sobolev space Discontinuous Galerkin method Finite element method Hp-refinement, Pollution effect Curved boundary edges LU factorization Fréchet differentiability Domain derivative Lipschitz boundary Implicit function theorem Newton method Tikhonov regularization Star domain Quadratic B-splines.

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