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Geometric and analytic aspects of functional variational principles = Cetraro, Italy 2022 /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Geometric and analytic aspects of functional variational principles/ by Rupert Frank ... [et al.].
其他題名:	Cetraro, Italy 2022 /
其他作者:	Frank, Rupert L.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	ix, 320 p. :ill., digital ;24 cm.
內容註:	- 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.
Contained By:	Springer Nature eBook
標題:	Functional analysis. -
電子資源:	https://doi.org/10.1007/978-3-031-67601-7
ISBN:	9783031676017

Geometric and analytic aspects of functional variational principles = Cetraro, Italy 2022 /
Geometric and analytic aspects of functional variational principlesCetraro, Italy 2022 /[electronic resource] :by Rupert Frank ... [et al.]. - Cham :Springer Nature Switzerland :2024. - ix, 320 p. :ill., digital ;24 cm. - Lecture ntes in mathematics,v. 23481617-9692 ;. - Lecture notes in mathematics ;v. 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.

ISBN: 9783031676017

Standard No.: 10.1007/978-3-031-67601-7doiSubjects--Topical Terms:

531838
Functional analysis.

LC Class. No.: QA320

Dewey Class. No.: 515.7

Geometric and analytic aspects of functional variational principles = Cetraro, Italy 2022 /
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520 $a 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.
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