HAIM BREZIS FUNCTIONAL ANALYSIS PDF

Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research. The English version is a welcome addition to this list. The first part of the text deals with abstract results in FA and operator theory. The second part is concerned with the study of spaces of functions of one or more real variables having specific differentiability properties, e.

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This process is experimental and the keywords may be updated as the learning algorithm improves. Dedicated to the memory of Professor K.

Yosida This is a preview of subscription content, log in to check access. Preview Unable to display preview. Download preview PDF. References [1] F. Lieb, Singularities of energy minimizing maps from the ball to the sphere: examples, counterexamples and bounds, Annals of Math. Bethuel, The approximation problem for Sobolev maps between manifolds, Acta Math. Brezis, Regularity of minimizers of relaxed problems for harmonic maps, J. Coron, Relaxed energies for harmonic maps, in Variational Problems H.

Berestycki, J. Coron and I. Ekeland ed. Google Scholar [6] F. Zheng, Density of smooth functions between two manifolds in Sobolev spaces, J. Ericksen and D. Kinderlehrer ed. Google Scholar [8] H. Giaquinta ed. Google Scholar [9] H. Lieb, Harmonic maps with defects, Comm.

Cladis, Defects in liquid crystals, Physics Today, May , 48— Google Scholar [11] P. Google Scholar [12] J. Lemaire, A report on harmonic maps, Bull. London Math. Google Scholar [14] C. Evans, Partial regularity for stationary harmonic maps into the sphere, Archive Rat. Soucek, Cartesian currents and variational problems for mappings into spheres, Ann. Pisa 16 , — Soucek, The Dirichlet energy of mappings with values into the sphere, Manuscripta Math. Hajlasz, Approximation of Sobolev mapping, Diff.

Google Scholar [18] R. Lin, A remark on H 1 mappings, Manuscripta Math. Poon, Axially symmetric harmonic maps minimizing a relaxed energy to appear. Google Scholar [20] D. Kinderlehrer, Recent developments in liquid crystal theory, Proc. Lions R. Dautray ed. Google Scholar [21] T. Uhlenbeck, A regularity theory for harmonic maps, J.

Serrin, On the definition and properties of certain variational integrals, Trans. Yosida, Functional Analysis, Springer Google Scholar Copyright information.

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