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001467766 001__ 1467766
001467766 003__ OCoLC
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001467766 019__ $$a1378384701
001467766 020__ $$a9789819906857$$q(electronic bk.)
001467766 020__ $$a9819906857$$q(electronic bk.)
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001467766 0247_ $$a10.1007/978-981-99-0685-7$$2doi
001467766 035__ $$aSP(OCoLC)1378390924
001467766 040__ $$aEBLCP$$beng$$cEBLCP$$dGW5XE$$dYDX$$dEBLCP
001467766 049__ $$aISEA
001467766 050_4 $$aQA601
001467766 08204 $$a515/.78$$223/eng/20230515
001467766 1001_ $$aAlicandro, Roberto.
001467766 24512 $$aA variational theory of convolution-type functionals /$$cRoberto Alicandro, Nadia Ansini, Andrea Braides, Andrey Piatnitski, Antonio Tribuzio.
001467766 260__ $$aSingapore :$$bSpringer,$$c2023.
001467766 300__ $$a1 online resource (121 p.).
001467766 4901_ $$aSpringerBriefs on PDEs and Data Science
001467766 504__ $$aIncludes bibliographical references and index.
001467766 5050_ $$aIntro -- Preface -- Contents -- 1 Introduction -- References -- 2 Convolution-Type Energies -- 2.1 Notation -- 2.2 Setting of the Problem and Comments -- 2.3 Assumptions -- Reference -- 3 The -Limit of a Class of Reference Energies -- 3.1 The -Limit of G[a] -- References -- 4 Asymptotic Embedding and Compactness Results -- 4.1 An Extension Result -- 4.2 Control of Long-Range Interactions with Short-Range Interactions -- 4.3 Compactness in Lp Spaces -- 4.4 Poincaré Inequalities -- References -- 5 A Compactness and Integral-Representation Result -- 5.1 The Integral-Representation Theorem
001467766 5058_ $$a5.2 Truncated-Range Functionals -- 5.3 Fundamental Estimates -- 5.4 Proof of the Integral-Representation Theorem -- 5.5 Convergence of Minimum Problems -- 5.6 Euler-Lagrange Equations -- 5.6.1 Regularity of Functionals F -- 5.6.2 Relations with Minimum Problems -- References -- 6 Periodic Homogenization -- 6.1 A Homogenization Theorem -- 6.2 The Convex Case -- 6.3 Relaxation of Convolution-Type Energies -- 6.4 An Extension Lemma from Periodic Lipschitz Domains -- 6.5 Homogenization on Perforated Domains -- References -- 7 A Generalization and Applications to Point Clouds
001467766 5058_ $$a7.1 Perturbed Convolution-Type Functionals -- 7.2 Application to Functionals Defined on Point Clouds -- References -- 8 Stochastic Homogenization -- References -- 9 Application to Convex Gradient Flows -- 9.1 The Minimizing-Movement Approach to Gradient Flows -- 9.2 Homogenized Flows for Convex Energies -- References -- Index
001467766 506__ $$aAccess limited to authorized users.
001467766 520__ $$aThis book provides a general treatment of a class of functionals modelled on convolution energies with kernel having finite p-moments. A general asymptotic analysis of such non-local functionals is performed, via Gamma-convergence, in order to show that the limit may be a local functional representable as an integral. Energies of this form are encountered in many different contexts and the interest in building up a general theory is also motivated by the multiple interests in applications (e.g. peridynamics theory, population dynamics phenomena and data science). The results obtained are applied to periodic and stochastic homogenization, perforated domains, gradient flows, and point-clouds models. This book is mainly intended for mathematical analysts and applied mathematicians who are also interested in exploring further applications of the theory to pass from a non-local to a local description, both in static problems and in dynamic problems.
001467766 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed May 15, 2023).
001467766 650_0 $$aConvolutions (Mathematics)
001467766 650_0 $$aVariational principles.
001467766 655_0 $$aElectronic books.
001467766 7001_ $$aAnsini, Nadia.
001467766 7001_ $$aBraides, Andrea.
001467766 7001_ $$aPi͡atnit͡skiĭ, A. L.$$q(Andreǐ L.),$$d1955-
001467766 7001_ $$aTribuzio, Antonio.
001467766 77608 $$iPrint version:$$aAlicandro, Roberto$$tA Variational Theory of Convolution-Type Functionals$$dSingapore : Springer,c2023$$z9789819906840
001467766 830_0 $$aSpringerBriefs on PDEs and data science.
001467766 852__ $$bebk
001467766 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-99-0685-7$$zOnline Access$$91397441.1
001467766 909CO $$ooai:library.usi.edu:1467766$$pGLOBAL_SET
001467766 980__ $$aBIB
001467766 980__ $$aEBOOK
001467766 982__ $$aEbook
001467766 983__ $$aOnline
001467766 994__ $$a92$$bISE