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Regularity of Free Boundaries in Obstacle-Type Problems

2012 Mathematics
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Release : 2012
Genre : Mathematics
Kind : eBook
Book Rating : 947/5 ( reviews)

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Book Synopsis Regularity of Free Boundaries in Obstacle-Type Problems by : Arshak Petrosyan

Download or read book Regularity of Free Boundaries in Obstacle-Type Problems written by Arshak Petrosyan. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Regularity of Free Boundaries in Obstacle-type Problems

Mathematics
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Release :
Genre : Mathematics
Kind : eBook
Book Rating : 923/5 ( reviews)

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Book Synopsis Regularity of Free Boundaries in Obstacle-type Problems by : Arshak Petrosyan

Download or read book Regularity of Free Boundaries in Obstacle-type Problems written by Arshak Petrosyan. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:

Free Boundary Problems

2018-09-20 Mathematics
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Release : 2018-09-20
Genre : Mathematics
Kind : eBook
Book Rating : 798/5 ( reviews)

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Book Synopsis Free Boundary Problems by : Darya Apushkinskaya

Download or read book Free Boundary Problems written by Darya Apushkinskaya. This book was released on 2018-09-20. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with several elliptic and parabolic obstacle-type problems with a focus on the cases where the free and fixed boundaries meet. The results presented complement those found in existing books in the subject, which mainly treat regularity properties away from the fixed boundary. The topics include optimal regularity, analysis of global solutions, tangential touch of the free and fixed boundaries, as well as Lipschitz- and $C^1$-regularity of the free boundary. Special attention is given to local versions of various monotonicity formulas. The intended audience includes research mathematicians and advanced graduate students interested in problems with free boundaries.

The obstacle problem

1999-10-01 Mathematics
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Release : 1999-10-01
Genre : Mathematics
Kind : eBook
Book Rating : 492/5 ( reviews)

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Book Synopsis The obstacle problem by : Luis Angel Caffarelli

Download or read book The obstacle problem written by Luis Angel Caffarelli. This book was released on 1999-10-01. Available in PDF, EPUB and Kindle. Book excerpt: The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.

Geometric Measure Theory and Free Boundary Problems

2021-03-23 Mathematics
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Release : 2021-03-23
Genre : Mathematics
Kind : eBook
Book Rating : 99X/5 ( reviews)

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Book Synopsis Geometric Measure Theory and Free Boundary Problems by : Guido De Philippis

Download or read book Geometric Measure Theory and Free Boundary Problems written by Guido De Philippis. This book was released on 2021-03-23. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro. Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.

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