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    • Plusieurs versions

    Analyse fonctionnelle : théorie et applications

    Brézis, Haïm
    • Livre
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    Functional analysis, Sobolev spaces and partial differential equations

    Brézis, Haïm
    New York ; London : Springer
    2011
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    Titre: Functional analysis, Sobolev spaces and partial differential equations / Haim Brezis
    Auteur: Brézis, Haïm
    Editeur: New York ; London : Springer
    Date: 2011
    Collation: xiii, 599 p. ; 24 cm.
    Collection: Universitext
    Documents dans cette collection: Universitext
    Sujet LCSH: Differential equations, Partial - Functional analysis - Sobolev spaces
    Contient: The Hahn-Banach theorems : introduction to the theory of conjugate convex functions -- The uniform boundedness principle and the closed graph theorem -- Weak topologies, reflexive spaces, separable spaces, uniform convexity -- Lp spaces -- Hilbert spaces -- Compact operators, spectral decomposition of self-adjoint compact operators -- The Hille-Yosida theorem -- Sobolev spaces and the variational formulation of boundary value problems in one dimension -- Sobolev spaces and the variational formulation of elliptic boundary value problems in N dimensions -- Evolution problems : the heat equation and the wave equation -- Miscellaneous complements
    Note: Originally published in French as Analyse fonctionelle, théorie et applications (Paris: Masson, c1983) ; this English edition contains revisions and added exercises - Includes bibliographical references (p. 585-594) and index.
    Classification: ams 46
    IMATH B-8
    Identifiant: 0387709134 (pbk.) (ISBN); 9780387709130 (pbk.) (ISBN)
    No RERO: R005934439
    Permalien:
    http://data.rero.ch/01-R005934439/html?view=FR_V1

    • Plusieurs versions

    Remarks on the Monge–Kantorovich problem in the discrete setting

    Brezis, Haïm
    Comptes rendus - Mathématique, February 2018, Vol.356(2), pp.207-213 [Revue évaluée par les pairs]
    ScienceDirect Journals (Elsevier)
    • Plusieurs versions

    Comments on two Notes by L. Ma and X. Xu

    Brezis, Haïm
    Comptes rendus - Mathématique, 2011, Vol.349(5), pp.269-271 [Revue évaluée par les pairs]

    • Plusieurs versions

    Density in Ws,p(Ω;N)

    Brezis, Haïm, Mironescu, Petru
    Journal of Functional Analysis, 01 October 2015, Vol.269(7), pp.2045-2109 [Revue évaluée par les pairs]

    • Plusieurs versions

    Minimizers of the W1,1-energy of S1-valued maps with prescribed singularities. Do they exist?

    Brezis, Haïm, Mironescu, Petru
    Nonlinear Analysis, December 2018, Vol.177, pp.105-134 [Revue évaluée par les pairs]
    ScienceDirect Journals (Elsevier)
    • Plusieurs versions

    Gagliardo–Nirenberg inequalities and non-inequalities: The full story

    Brezis, Haïm, Mironescu, Petru
    Annales de l'Institut Henri Poincaré / Analyse non linéaire, August 2018, Vol.35(5), pp.1355-1376 [Revue évaluée par les pairs]

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    Haïm Brezis, un mathématicien juif : entretien avec Jacques Vauthier

    Brézis, Haïm
    Vauthier, Jacques
    Paris : Beauchesne
    1999
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    Titre: Haïm Brezis, un mathématicien juif : entretien avec Jacques Vauthier
    Auteur: Brézis, Haïm
    Contributeur: Vauthier, Jacques
    Editeur: Paris : Beauchesne
    Date: 1999
    Collation: 145 p. : ill. ; 22 cm
    Collection: Scientifiques & croyants ; 8
    Documents dans cette collection: Scientifiques [et] croyants
    Sujet RERO: Christianisme - Judaïsme - Mathématiques - Brezis, Haïm
    Sujet RERO - forme: [Entretiens]
    Identifiant: 2701013356 (ISBN)
    No RERO: R264805360
    Permalien:
    http://data.rero.ch/01-R264805360/html?view=FR_V1

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    On the Optimality of Shape and Data Representation in the Spectral Domain

    Aflalo, Yonathan, Brezis, Haim, Kimmel, Ron
    SIAM Journal on Imaging Sciences, 2015, Vol.8(2), pp.1141-1160 [Revue évaluée par les pairs]
    SIAM Journals (Society for Industrial and Applied Mathematics), Copyright �� by the Society of Industrial and Applied Mathematics, Philadelphia, PA
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    Titre: On the Optimality of Shape and Data Representation in the Spectral Domain
    Auteur: Aflalo, Yonathan; Brezis, Haim; Kimmel, Ron
    Sujet: Laplace--Beltrami ; Shape Analysis ; Principal Component Analysis ; 43a77
    Description: A proof of the optimality of the eigenfunctions of the Laplace--Beltrami operator (LBO) in representing smooth functions on surfaces is provided and adapted to the field of applied shape and data analysis. It is based on the Courant--Fischer min-max principle adapted to our case. The theorem we present supports the new trend in geometry processing of treating geometric structures by using their projection onto the leading eigenfunctions of the decomposition of the LBO. Utilization of this result can be used for constructing numerically efficient algorithms to process shapes in their spectrum. We review a couple of applications as possible practical usage cases of the proposed optimality criteria. We refer to a scale invariant metric, which is also invariant to bending of the manifold. This novel pseudometric allows constructing an LBO by which a scale invariant eigenspace on the surface is defined. We demonstrate the efficiency of an intermediate metric, defined as an interpolation between the scale invariant and the regular one, in representing geometric structures while capturing both coarse and fine details. Next, we review a numerical acceleration technique for classical scaling, a member of a family of flattening methods known as multidimensional scaling (MDS). There, the optimality is exploited to efficiently approximate all geodesic distances between pairs of points on a given surface and thereby match and compare between almost isometric surfaces. Finally, we revisit the classical principal component analysis (PCA) definition by coupling its variational form with a Dirichlet energy on the data manifold. By pairing the PCA with the LBO we can efficiently handle cases that go beyond the scope defined by the observation set that is handled by regular PCA.
    Fait partie de: SIAM Journal on Imaging Sciences, 2015, Vol.8(2), pp.1141-1160
    Identifiant: 1936-4954 (E-ISSN); 10.1137/140977680 (DOI)

    • Plusieurs versions

    Non-local Functionals Related to the Total Variation and Connections with Image Processing

    Brezis, Haïm, Nguyen, Hoai-Minh
    Annals of PDE, 2018, Vol.4(1), pp.1-77 [Revue évaluée par les pairs]