LEADER 03505nam 22006495 450 001 996630872603316 005 20250808090310.0 010 $a9783031676017 010 $a3031676017 024 7 $a10.1007/978-3-031-67601-7 035 $a(CKB)36619456100041 035 $a(MiAaPQ)EBC31787983 035 $a(Au-PeEL)EBL31787983 035 $a(OCoLC)1472981671 035 $a(DE-He213)978-3-031-67601-7 035 $a(PPN)281830436 035 $a(EXLCZ)9936619456100041 100 $a20241120d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric and Analytic Aspects of Functional Variational Principles $eCetraro, Italy 2022 /$fby Rupert Frank, Giuseppe Mingione, Lubos Pick, Ovidiu Savin, Jean Van Schaftingen ; edited by Andrea Cianchi, Vladimir Maz'ya, Tobias Weth 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (325 pages) 225 1 $aC.I.M.E. Foundation Subseries,$x2946-1820 ;$v2348 311 08$a9783031676000 311 08$a3031676009 327 $a- The Sharp Sobolev Inequality and its Stability: An Introduction -- Nonlinear Potential Theoretic Methods in Nonuniformly Elliptic Problems -- Reduction Principles -- The Monge-Ampere Equation -- Injective Ellipticity, Cancelling Operators, and Endpoint Gagliardo-Nirenberg-Sobolev Inequalities for Vector Fields. 330 $aThis book is dedicated to exploring optimization problems of geometric-analytic nature, which are fundamental to tackling various unresolved questions in mathematics and physics. These problems revolve around minimizing geometric or analytic quantities, often representing physical energies, within prescribed collections of sets or functions. They serve as catalysts for advancing methodologies in calculus of variations, partial differential equations, and geometric analysis. Furthermore, insights from optimal functional-geometric inequalities enhance analytical problem-solving endeavors. The contributions focus on the intricate interplay between these inequalities and problems of differential and variational nature. Key topics include functional and geometric inequalities, optimal norms, sharp constants in Sobolev-type inequalities, and the regularity of solutions to variational problems. Readers will gain a comprehensive understanding of these concepts, deepening their appreciation for their relevance in mathematical and physical inquiries. 410 0$aC.I.M.E. Foundation Subseries,$x2946-1820 ;$v2348 606 $aMathematical analysis 606 $aDifferential equations 606 $aAnalysis 606 $aDifferential Equations 615 0$aMathematical analysis. 615 0$aDifferential equations. 615 14$aAnalysis. 615 24$aDifferential Equations. 676 $a515 700 $aCianchi$b Andrea$0722498 701 $aMaz'ya$b Vladimir$061872 701 $aWeth$b Tobias$01775334 701 $aFrank$b Rupert$01775335 701 $aMingione$b Giuseppe$01775336 701 $aPick$b Lubos$01705715 701 $aSavin$b Ovidiu$01775337 701 $aVan Schaftingen$b Jean$01775338 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996630872603316 996 $aGeometric and Analytic Aspects of Functional Variational Principles$94289936 997 $aUNISA