<p>This is a completely revised English edition of the important Analyse fonctionnelle (1983). It contains a wealth of problems and exercises to guide the reader. It is also the first single-volume textbook to cover related fields of functional analysis and PDEs.</p>

Functional Analysis, Sobolev Spaces and Partial Differential Equations (Universitext)

Science & Math

Brezis, Haïm

Mathematics

Springer

Contains papers presented by leading international experts at the well-established weekly seminar held at the College de France.

Nonlinear Partial Differential Equations and Their Applications: College de France Seminars (Nonlinear Partial Differential Equations & Their Application)

Brezis, H.

John Wiley&Sons

Nonlinear Partial Differential Equations and Their ApplicationsCollge de France Seminar Volume XI (Chapman & Hall/CRC Research Notes in Mathematics Series)

Lions, Jacques-Louis

Chapman and Hall/CRC

The original motivation of this study comes from the following questions that were mentioned to one ofus by H. Matano. Let 2 2 G= B = {x=(X1lX2) E 2 ; x~ + x~ = Ixl < 1}. 1 Consider the Ginzburg-Landau functional 2 2 (1) E~(u) = ~ LIVul + 4~2 L(lu1 _1)2 which is defined for maps u E H1(G;C) also identified with Hl(G;R2). Fix the boundary condition 9(X) =X on 8G and set H; = {u E H1(G;C); u = 9 on 8G}. It is easy to see that (2) is achieved by some u~ that is smooth and satisfies the Euler equation in G, -~u~ = :2 u~(1 _lu~12) (3) { on aGo u~ =9 Themaximum principleeasily implies (see e.g., F. Bethuel, H. Brezisand F. Helein (2]) that any solution u~ of (3) satisfies lu~1 ~ 1 in G. In particular, a subsequence (u~,.) converges in the w* - LOO(G) topology to a limit u*.

Ginzburg-Landau Vortices (Progress in Nonlinear Differential Equations and Their Applications, 13)

Hélein, Frédéric

Bethuel, Fabrice

Birkhauser

<p><div>The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifold-valued Sobolev maps is relatively new. The incentive to explore these spaces arose in the last forty years from geometry and physics.&nbsp; This monograph is the first to provide a unified, comprehensive treatment of Sobolev maps to the circle, presenting numerous results obtained by the authors and others. Many surprising connections to other areas of mathematics are explored, including the Monge-Kantorovich theory in optimal transport, items in geometric measure theory, Fourier series, and non-local functionals occurring, for example, as denoising filters in image processing. Numerous digressions provide a glimpse of the theory of sphere-valued Sobolev maps.&nbsp;</div> <br /> <div>Each chapter focuses on a single topic and starts with a detailed overview, followed by the most significant results, and rather complete proofs. The "Complements and Open Problems" sections provide short introductions to various subsequent developments or related topics, and suggest new</div> <div>directions of research.&nbsp; Historical perspectives and a comprehensive list of references close out each chapter.&nbsp; Topics covered include lifting, point and line singularities, minimal connections and minimal surfaces, uniqueness spaces, factorization, density, Dirichlet problems, trace theory, and gap phenomena.</div> <div><br /></div> <div><i>Sobolev Maps to the Circle</i> will appeal to mathematicians working in various areas, such as nonlinear analysis, PDEs, geometric analysis, minimal surfaces, optimal transport, and topology.&nbsp; It will also be of interest to physicists working on liquid crystals and the Ginzburg-Landau theory of superconductors.</div> <div><br /></div></p>

Sobolev Maps to the Circle: From the Perspective of Analysis, Geometry, and Topology (Progress in Nonlinear Differential Equations and Their Applications, 96)

Mironescu, Petru

Analyse fonctionnelle - Théorie et applications: Théorie et applications

Dunod]

Haim Brezis: Un mathematicien Juif (Coll. Scientifiques & croyants)

Biographies & Memoirs

Vauthier, Jacques

Professionals & Academics

BEAUCHESNE

Análisis funcional (Spanish Edition)

Alianza Editorial

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