Geometric and analytic aspects of functional variational principles : Cetraro, Italy 2022 / Rupert Frank, Giuseppe Mingione, Lubos Pick, Ovidiu Savin, Jean Van Schaftingen ; Andrea Cianchi, Vladimir Maz'ya, Tobias Weth, editors.

Format:

Book

Author/Creator:

Frank, Rupert L., author.

Mingione, Giuseppe, 1972- author.

Pick, Luboš, author.

Savin, Vasile Ovidiu, 1977- author.

Contributor:

Van Schaftingen, Jean, editor.

Cianchi, Andrea, editor.

Mazʹi︠a︡, V. G., editor.

Weth, Tobias, editor.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2348.

Lecture notes in mathematics (Springer-Verlag). CIME Foundation subseries 2946-1812

Lecture notes in mathematics, 0075-8434 ; volume 2348. C.I.M.E. foundation subseries, 2946-1812

Language:

English

Subjects (All):

Functional analysis.

Differential equations, Partial.

Physical Description:

ix, 317 pages : illustrations ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2024]

Summary:

"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"--Publisher's description.

Contents:

1. The Sharp Sobolev Inequality and its Stability: An Introduction / Rupert L. Frank

2. Nonlinear Potential Theoretic Methods in Nonuniformly Elliptic Problems / Giuseppe Mingione

3. Reduction Principles / Luboš Pick

The Monge-Ampère Equation / Ovidiu Savin

Injective Ellipticity, Cancelling Operators, and Endpoint Gagliardo-Nirenberg-Sobolev Inequalities for Vector Fields / Jean Van Schaftingen.

Notes:

"Extended version of a series of lectures given at the CIME Summer School in Centraro in June 2022"--Page 1.

Includes bibliographical references.

ISBN:

9783031676000

3031676009

OCLC:

1479205728