001441421 000__ 04235cam\a2200505Ii\4500
001441421 001__ 1441421
001441421 003__ OCoLC
001441421 005__ 20230309004738.0
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001441421 019__ $$a1295849604
001441421 020__ $$a9781071615126$$q(electronic bk.)
001441421 020__ $$a1071615122$$q(electronic bk.)
001441421 020__ $$z9781071615102$$q(print)
001441421 0247_ $$a10.1007/978-1-0716-1512-6$$2doi
001441421 035__ $$aSP(OCoLC)1290721171
001441421 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dYDX$$dOCLCO$$dOCLCF$$dN$T$$dOCLCO$$dOCLCQ
001441421 049__ $$aISEA
001441421 050_4 $$aQA323
001441421 08204 $$a515/.782$$223
001441421 1001_ $$aBrézis, H.$$q(Haim),$$eauthor.
001441421 24510 $$aSobolev maps to the circle :$$bfrom the perspective of analysis, geometry, and topology /$$cHaïm Brezis, Petru Mironescu.
001441421 264_1 $$aNew York, NY :$$bBirkhäuser,$$c2021.
001441421 300__ $$a1 online resource (xxxi, 530 pages) :$$billustrations (some color).
001441421 336__ $$atext$$btxt$$2rdacontent
001441421 337__ $$acomputer$$bc$$2rdamedia
001441421 338__ $$aonline resource$$bcr$$2rdacarrier
001441421 4901_ $$aProgress in nonlinear differential equations and their applications,$$x2374-0280 ;$$vvolume 96
001441421 504__ $$aIncludes bibliographical references and indexes.
001441421 5050_ $$aLifting in $W^{1,p}$ -- The Geometry of $J(u)$ and $\Sigma(u)$ in 2D; Point Singularities and Minimal Connections -- The Geometry of $J(u)$ and $\Sigma(u)$ in 3D (and higher); Line Singularities and Minimal Surfaces -- A Digression: Sphere-Valued Maps -- Lifting in Fractional Sobolev Spaces and in $VMO$ -- Uniqueness of Lifting and Beyond -- Factorization -- Applications of the Factorization -- Estimates of Phases: Positive and Negative Results -- Density -- Traces -- Degree -- Dirichlet Problems, Gaps, Infinite Energies -- Domains with Topology -- Appendices.
001441421 506__ $$aAccess limited to authorized users.
001441421 520__ $$aThe 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. 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. 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 directions of research. Historical perspectives and a comprehensive list of references close out each chapter. Topics covered include lifting, point and line singularities, minimal connections and minimal surfaces, uniqueness spaces, factorization, density, Dirichlet problems, trace theory, and gap phenomena. Sobolev Maps to the Circle will appeal to mathematicians working in various areas, such as nonlinear analysis, PDEs, geometric analysis, minimal surfaces, optimal transport, and topology. It will also be of interest to physicists working on liquid crystals and the Ginzburg-Landau theory of superconductors.
001441421 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed January 4, 2022).
001441421 650_0 $$aSobolev spaces.
001441421 650_6 $$aEspaces de Sobolev.
001441421 655_0 $$aElectronic books.
001441421 7001_ $$aMironescu, Petru,$$eauthor.
001441421 830_0 $$aProgress in nonlinear differential equations and their applications ;$$vv. 96.$$x2374-0280
001441421 852__ $$bebk
001441421 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-1-0716-1512-6$$zOnline Access$$91397441.1
001441421 909CO $$ooai:library.usi.edu:1441421$$pGLOBAL_SET
001441421 980__ $$aBIB
001441421 980__ $$aEBOOK
001441421 982__ $$aEbook
001441421 983__ $$aOnline
001441421 994__ $$a92$$bISE