03505nam 22006495 450 99663087260331620250808090310.09783031676017303167601710.1007/978-3-031-67601-7(CKB)36619456100041(MiAaPQ)EBC31787983(Au-PeEL)EBL31787983(OCoLC)1472981671(DE-He213)978-3-031-67601-7(PPN)281830436(EXLCZ)993661945610004120241120d2024 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierGeometric and Analytic Aspects of Functional Variational Principles Cetraro, Italy 2022 /by Rupert Frank, Giuseppe Mingione, Lubos Pick, Ovidiu Savin, Jean Van Schaftingen ; edited by Andrea Cianchi, Vladimir Maz'ya, Tobias Weth1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Springer,2024.1 online resource (325 pages)C.I.M.E. Foundation Subseries,2946-1820 ;23489783031676000 3031676009 - 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.This 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.C.I.M.E. Foundation Subseries,2946-1820 ;2348Mathematical analysisDifferential equationsAnalysisDifferential EquationsMathematical analysis.Differential equations.Analysis.Differential Equations.515Cianchi Andrea722498Maz'ya Vladimir61872Weth Tobias1775334Frank Rupert1775335Mingione Giuseppe1775336Pick Lubos1705715Savin Ovidiu1775337Van Schaftingen Jean1775338MiAaPQMiAaPQMiAaPQBOOK996630872603316Geometric and Analytic Aspects of Functional Variational Principles4289936UNISA