Henrik Shahgholian's Books

Regularity of Free Boundaries in Obstacle-Type Problems

By: Arshak Petrosyan,Henrik Shahgholian,Nina Nikolaevna Uralʹt︠s︡eva

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Regularity of Free Boundaries in Obstacle-Type Problems

By: Arshak Petrosyan,Henrik Shahgholian,Nina Nikolaevna Uralʹt︠s︡eva

The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as well as in applications. Since then the theory continued to evolve. Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems. The emphasis is on the methods developed in the past two decades. The topics include optimal regularity, nondegeneracy, rescalings and blowups, classification of global solutions, several types of monotonicity formulas, Lipschitz, $C^1$, as well as higher regularity of the free boundary, structure of the singular set, touch of the free and fixed boundaries, and more. The book is based on lecture notes for the courses and mini-courses given by the authors at various locations and should be accessible to advanced graduate students and researchers in analysis and partial differential equations.

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Page Count

233

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821887947

ISBN 13

9780821887943

Geometry of PDEs and Related Problems

Cetraro, Italy 2017

By: Xavier Cabré,Antoine Henrot,Daniel Peralta-Salas,Wolfgang Reichel,Henrik Shahgholian

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Geometry of PDEs and Related Problems

Cetraro, Italy 2017

By: Xavier Cabré,Antoine Henrot,Daniel Peralta-Salas,Wolfgang Reichel,Henrik Shahgholian

The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing up-to-date references. Collecting together the lecture notes of the five mini-courses given at the CIME Summer School held in Cetraro (Cosenza, Italy) in the week of June 19–23, 2017, the volume presents a friendly introduction to a broad spectrum of up-to-date and hot topics in the study of PDEs, describing the state-of-the-art in the subject. It also gives further details on the main ideas of the proofs, their technical difficulties, and their possible extension to other contexts. Aiming to be a primary source for researchers in the field, the book will attract potential readers from several areas of mathematics.

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Page Count

207

Publisher

Springer

Published Date

ISBN 10

3319951866

ISBN 13

9783319951867

Geometry of PDEs and Related Problems

Cetraro, Italy 2017

By: Xavier Cabré,Antoine Henrot,Daniel Peralta-Salas,Wolfgang Reichel,Henrik Shahgholian

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Geometry of PDEs and Related Problems

Cetraro, Italy 2017

By: Xavier Cabré,Antoine Henrot,Daniel Peralta-Salas,Wolfgang Reichel,Henrik Shahgholian

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N/A

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Solve jigsaw puzzle

Age

Page Count

207

Publisher

Springer

Published Date

ISBN 10

3319951866

ISBN 13

9783319951867

Book's by Henrik Shahgholian

Regularity of Free Boundaries in Obstacle-Type Problems

Regularity of Free Boundaries in Obstacle-Type Problems

Geometry of PDEs and Related Problems

Geometry of PDEs and Related Problems

Geometry of PDEs and Related Problems

Geometry of PDEs and Related Problems

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