Regularity Of The One Phase Free Boundaries

Author : Bozhidar Velichkov
Publisher : Springer Nature
Page : 249 pages
File Size : 51,6 Mb
Release : 2023-02-24
Category : Mathematics
ISBN : 9783031132384

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Regularity of the One-phase Free Boundaries by Bozhidar Velichkov Pdf

This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive research. The exposition is organized around four main theorems, which are dedicated to the one-phase functional in its simplest form. Many of the methods and the techniques presented here are very recent and were developed in the context of different free boundary problems. We also give the detailed proofs of several classical results, which are based on some universal ideas and are recurrent in the free boundary, PDE and the geometric regularity theories. This book is aimed at graduate students and researches and is accessible to anyone with a moderate level of knowledge of elliptical PDEs.

Author : Darya Apushkinskaya
Publisher : Springer
Page : 146 pages
File Size : 41,5 Mb
Release : 2018-09-20
Category : Mathematics
ISBN : 9783319970790

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Free Boundary Problems by Darya Apushkinskaya Pdf

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.

Author : Arshak Petrosyan,Henrik Shahgholian,Nina Nikolaevna Uralʹt︠s︡eva
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 48,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821887943

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Regularity of Free Boundaries in Obstacle-Type Problems by Arshak Petrosyan,Henrik Shahgholian,Nina Nikolaevna Uralʹt︠s︡eva Pdf

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.

Author : Luis Angel Caffarelli
Publisher : Edizioni della Normale
Page : 0 pages
File Size : 44,5 Mb
Release : 1999-10-01
Category : Mathematics
ISBN : 8876422498

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The obstacle problem by Luis Angel Caffarelli Pdf

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.

Author : Giovanna Citti,Maria Manfredini,Daniele Morbidelli,Sergio Polidoro,Francesco Uguzzoni
Publisher : Springer
Page : 373 pages
File Size : 52,6 Mb
Release : 2015-10-31
Category : Mathematics
ISBN : 9783319026664

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Geometric Methods in PDE’s by Giovanna Citti,Maria Manfredini,Daniele Morbidelli,Sergio Polidoro,Francesco Uguzzoni Pdf

The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications.

Author : Tadele Mengesha,Abner J. Salgado
Publisher : Springer Nature
Page : 325 pages
File Size : 51,7 Mb
Release : 2023-09-12
Category : Mathematics
ISBN : 9783031340895

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A3N2M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models by Tadele Mengesha,Abner J. Salgado Pdf

This volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.

Author : Abbas Bahri,Sergiu Klainerman,Michael Vogelius
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 53,8 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821836354

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Noncompact Problems at the Intersection of Geometry, Analysis, and Topology by Abbas Bahri,Sergiu Klainerman,Michael Vogelius Pdf

This proceedings volume contains articles from the conference held at Rutgers University in honor of Haim Brezis and Felix Browder, two mathematicians who have had a profound impact on partial differential equations, functional analysis, and geometry. Mathematicians attending the conference had interests in noncompact variational problems, pseudo-holomorphic curves, singular and smooth solutions to problems admitting a conformal (or some group) invariance, Sobolev spaces on manifolds, and configuration spaces. One day of the proceedings was devoted to Einstein equations and related topics. Contributors to the volume include, among others, Sun-Yung A. Chang, Luis A. Caffarelli, Carlos E. Kenig, and Gang Tian. The material is suitable for graduate students and researchers interested in problems in analysis and differential equations on noncompact manifolds.

Author : Donatella Danielli,Arshak Petrosyan,Camelia A. Pop
Publisher : American Mathematical Soc.
Page : 214 pages
File Size : 48,7 Mb
Release : 2019-02-21
Category : Differential equations
ISBN : 9781470441104

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New Developments in the Analysis of Nonlocal Operators by Donatella Danielli,Arshak Petrosyan,Camelia A. Pop Pdf

This volume contains the proceedings of the AMS Special Session on New Developments in the Analysis of Nonlocal Operators, held from October 28–30, 2016, at the University of St. Thomas, Minneapolis, Minnesota. Over the last decade there has been a resurgence of interest in problems involving nonlocal operators, motivated by applications in many areas such as analysis, geometry, and stochastic processes. Problems represented in this volume include uniqueness for weak solutions to abstract parabolic equations with fractional time derivatives, the behavior of the one-phase Bernoulli-type free boundary near a fixed boundary and its relation to a Signorini-type problem, connections between fractional powers of the spherical Laplacian and zeta functions from the analytic number theory and differential geometry, and obstacle problems for a class of not stable-like nonlocal operators for asset price models widely used in mathematical finance. The volume also features a comprehensive introduction to various aspects of the fractional Laplacian, with many historical remarks and an extensive list of references, suitable for beginners and more seasoned researchers alike.

Author : Luis A. Caffarelli,S. Salsa
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 45,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837849

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A Geometric Approach to Free Boundary Problems by Luis A. Caffarelli,S. Salsa Pdf

We hope that the tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems."--Jacket.

Author : Anonim
Publisher : Unknown
Page : 898 pages
File Size : 53,5 Mb
Release : 1986
Category : Computable functions
ISBN : UOM:39015036980939

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Transactions of the ... Army Conference on Applied Mathematics and Computing by Anonim Pdf

Author : Darya Apushkinskaya,Alexander I. Nazarov
Publisher : American Mathematical Society
Page : 282 pages
File Size : 51,8 Mb
Release : 2014-08-22
Category : Mathematics
ISBN : 9781470415518

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Proceedings of the St. Petersburg Mathematical Society, Volume XV by Darya Apushkinskaya,Alexander I. Nazarov Pdf

This book presents the proceedings of the international workshop, "Advances in Mathematical Analysis of Partial Differential Equations" held at the Institut Mittag-Leffler, Stockholm, Sweden, July 9-13, 2012, dedicated to the memory of the outstanding Russian mathematician Olga A. Ladyzhenskaya. The volume contains papers that engage a wide set of modern topics in the theory of linear and nonlinear partial differential equations and applications, including variational and free boundary problems, mathematical problems of hydrodynamics, and magneto-geostrophic equations.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 49,8 Mb
Release : 2005
Category : Mathematics
ISBN : 0821839276

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Selected Papers on Differential Equations and Analysis by Anonim Pdf

This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics, including differential equations with free boundary, singular integral operators, operator algebras, and relations between the Brownian motion on a manifold with function theory. The volume is suitable for graduate students and research mathematicians interested in analysis and differential equations."

Author : S.C. Gupta
Publisher : Elsevier
Page : 752 pages
File Size : 53,5 Mb
Release : 2017-07-27
Category : Science
ISBN : 9780444635822

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The Classical Stefan Problem by S.C. Gupta Pdf

The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, New Edition, provides the fundamental theory, concepts, modeling, and analysis of the physical, mathematical, thermodynamical, and metallurgical properties of classical Stefan and Stefan-like problems as applied to heat transfer problems with phase-changes, such as from liquid to solid. This self-contained work reports and derives the results from tensor analysis, differential geometry, non-equilibrium thermodynamics, physics, and functional analysis, and is thoroughly enriched with many appropriate references for in-depth background reading on theorems. Each chapter in this fully revised and updated edition begins with basic concepts and objectives, also including direction on how the subject matter was developed. It contains more than 400 pages of new material on quasi-analytical solutions and methods of classical Stefan and Stefan-like problems.The book aims to bridge the gap between the theoretical and solution aspects of the afore-mentioned problems. Provides both the phenomenology and mathematics of Stefan problems Bridges physics and mathematics in a concrete and readable manner Presents well-organized chapters that start with proper definitions followed by explanations and references for further reading Includes both numerical and quasi-analytical solutions and methods of classical Stefan and Stefan-like problems

Author : Thomas Y. Hou,Eitan Tadmor
Publisher : Springer Science & Business Media
Page : 946 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642557118

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Hyperbolic Problems: Theory, Numerics, Applications by Thomas Y. Hou,Eitan Tadmor Pdf

The International Conference on "Hyperbolic Problems: Theory, Numerics and Applications'' was held in CalTech on March 25-30, 2002. The conference was the ninth meeting in the bi-annual international series which became one of the highest quality and most successful conference series in Applied mathematics. This volume contains more than 90 contributions presented in this conference, including plenary presentations by A. Bressan, P. Degond, R. LeVeque, T.-P. Liu, B. Perthame, C.-W. Shu, B. Sjögreen and S. Ukai. Reflecting the objective of series, the contributions in this volume keep the traditional blend of theory, numerics and applications. The Hyp2002 meeting placed a particular emphasize on fundamental theory and numerical analysis, on multi-scale analysis, modeling and simulations, and on geophysical applications and free boundary problems arising from materials science and multi-component fluid dynamics. The volume should appeal to researchers, students and practitioners with general interest in time-dependent problems governed by hyperbolic equations.

Author : Guido De Philippis,Xavier Ros-Oton,Georg S. Weiss
Publisher : Springer Nature
Page : 138 pages
File Size : 45,6 Mb
Release : 2021-03-23
Category : Mathematics
ISBN : 9783030657994

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Geometric Measure Theory and Free Boundary Problems by Guido De Philippis,Xavier Ros-Oton,Georg S. Weiss Pdf

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.