LEADER 03115nam 2200505 450 001 9910768473303321 005 20230801215638.0 010 $a9789819906857$b(electronic bk.) 010 $z9789819906840 024 7 $a10.1007/978-981-99-0685-7 035 $a(MiAaPQ)EBC7244259 035 $a(Au-PeEL)EBL7244259 035 $a(DE-He213)978-981-99-0685-7 035 $a(OCoLC)1378390924 035 $a(PPN)270617256 035 $a(EXLCZ)9926561914600041 100 $a20230801d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Variational Theory of Convolution-Type Functionals /$fRoberto Alicandro [and four others] 205 $aFirst edition. 210 1$aSingapore :$cSpringer, Springer Nature Singapore Pte Ltd.,$d[2023] 210 4$dİ2023 215 $a1 online resource (121 pages) 225 0 $aSpringerBriefs on PDEs and Data Science Series 311 08$aPrint version: Alicandro, Roberto A Variational Theory of Convolution-Type Functionals Singapore : Springer,c2023 9789819906840 320 $aIncludes bibliographical references and index. 327 $aChapter 1. Introduction -- Chapter 2. Convolution-Type Energies -- Chapter 3. The ?-limit of a Class of Reference Energies -- Chapter 4. Asymptotic Embedding and Compactness Results -- Chapter 5. A Compactness and Integral-Representation Result -- Chapter 6. Periodic Homogenization -- Chapter 7. A Generalization and Applications to Point Clouds -- Chapter 8. Stochastic Homogenization -- Chapter 9. Application to Convex Gradient Flows. 330 $aThis book provides a general treatment of a class of functionals modelled on convolution energies with kernel having finite p-moments. A general asymptotic analysis of such non-local functionals is performed, via Gamma-convergence, in order to show that the limit may be a local functional representable as an integral. Energies of this form are encountered in many different contexts and the interest in building up a general theory is also motivated by the multiple interests in applications (e.g. peridynamics theory, population dynamics phenomena and data science). The results obtained are applied to periodic and stochastic homogenization, perforated domains, gradient flows, and point-clouds models. This book is mainly intended for mathematical analysts and applied mathematicians who are also interested in exploring further applications of the theory to pass from a non-local to a local description, both in static problems and in dynamic problems. . 410 0$aSpringerBriefs on PDEs and Data Science,$x2731-7609 606 $aConvolutions (Mathematics) 606 $aVariational principles 615 0$aConvolutions (Mathematics) 615 0$aVariational principles. 676 $a515.78 700 $aAlicandro$b Roberto$01457371 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910768473303321 996 $aA Variational Theory of Convolution-Type Functionals$93657904 997 $aUNINA