Geometric and Analytic Aspects of Functional Variational Principles: Cetraro, Italy 2022 (C.I.M.E. Foundation Subseries) - Softcover

Frank, Rupert; Mingione, Giuseppe; Pick, Lubos; Savin, Ovidiu; Van Schaftingen, Jean

Softcover

ISBN 10: 3031676009 ISBN 13: 9783031676000

Publisher: Springer, 2024

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2024
• Language: English
• ISBN 10: 3031676009
• ISBN 13: 9783031676000
• Binding: Paperback
• Number of pages: 332
• Editor: Cianchi Andrea, Maz'ya Vladimir, Weth Tobias