04028nam a22006015i 4500 978-3-031-67601-7 DE-He213 20251030113320.0 cr nn 008mamaa 241120s2024 sz | s |||| 0|eng d 9783031676017 978-3-031-67601-7 10.1007/978-3-031-67601-7 doi QA299.6-433 PBK bicssc MAT034000 bisacsh PBK thema Frank, Rupert. author. aut http://id.loc.gov/vocabulary/relators/aut 87768 Geometric and Analytic Aspects of Functional Variational Principles [electronic resource] : Cetraro, Italy 2022 / by Rupert Frank, Giuseppe Mingione, Lubos Pick, Ovidiu Savin, Jean Van Schaftingen ; edited by Andrea Cianchi, Vladimir Maz'ya, Tobias Weth. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. IX, 320 p. 9 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda C.I.M.E. Foundation Subseries, 2946-1820 ; 2348 - 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. Mathematical analysis. 64178 Differential equations. Analysis. Differential Equations. Mingione, Giuseppe. author. aut http://id.loc.gov/vocabulary/relators/aut 87769 Pick, Lubos. author. aut http://id.loc.gov/vocabulary/relators/aut 87770 Savin, Ovidiu. author. aut http://id.loc.gov/vocabulary/relators/aut 87771 Van Schaftingen, Jean. author. aut http://id.loc.gov/vocabulary/relators/aut 87772 Cianchi, Andrea. editor. edt http://id.loc.gov/vocabulary/relators/edt 87773 Maz'ya, Vladimir. editor. edt http://id.loc.gov/vocabulary/relators/edt 87774 Weth, Tobias. editor. edt http://id.loc.gov/vocabulary/relators/edt 87775 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031676000 Printed edition: 9783031676024 C.I.M.E. Foundation Subseries, 2946-1820 ; 2348 85459 https://doi.org/10.1007/978-3-031-67601-7 ZDB-2-SMA ZDB-2-SXMS ZDB-2-LNM 65076 65076