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Author : Luis A. Caffarelli,Sandro Salsa,S. Salsa
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 50,8 Mb
Release : 2005
Category : Boundary value problems
ISBN : 9780821837849
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 : Eduardo V. Teixeira
Publisher : de Gruyter
Page : 312 pages
File Size : 48,9 Mb
Release : 2020-01-13
Category : Mathematics
ISBN : 3110574489
This book offers a comprehensive introduction to modern techniques in the study of free boundary problems of diffusive type. Applications of such methods are thoroughly explained by emblematic examples of the theory and several geometric ideas and insights are carefully discussed, making the text both accessible and appealing to a broad readership working in partial differential equations, calculus of variations, and geometric analysis.
Author : Ioannis Athanasopoulos
Publisher : Routledge
Page : 366 pages
File Size : 48,7 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9781351447140
Free boundary problems arise in an enormous number of situations in nature and technology. They hold a strategic position in pure and applied sciences and thus have been the focus of considerable research over the last three decades. Free Boundary Problems: Theory and Applications presents the work and results of experts at the forefront of current research in mathematics, material sciences, chemical engineering, biology, and physics. It contains the plenary lectures and contributed papers of the 1997 International Interdisciplinary Congress proceedings held in Crete. The main topics addressed include free boundary problems in fluid and solid mechanics, combustion, the theory of filtration, and glaciology. Contributors also discuss material science modeling, recent mathematical developments, and numerical analysis advances within their presentations of more specific topics, such as singularities of interfaces, cusp cavitation and fracture, capillary fluid dynamics of film coating, dynamics of surface growth, phase transition kinetics, and phase field models. With the implications of free boundary problems so far reaching, it becomes important for researchers from all of these fields to stay abreast of new developments. Free Boundary Problems: Theory and Applications provides the opportunity to do just that, presenting recent advances from more than 50 researchers at the frontiers of science, mathematics, and technology.
Author : A. Bossavit,M. Fremond
Publisher : Unknown
Page : 334 pages
File Size : 45,7 Mb
Release : 1985
Category : Mathematics
ISBN : UCR:31210012400642
Author : Guido De Philippis,Xavier Ros-Oton,Georg S. Weiss
Publisher : Springer Nature
Page : 138 pages
File Size : 44,5 Mb
Release : 2021-03-23
Category : Mathematics
ISBN : 9783030657994
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.
Author : J I Diaz,Juan Luis Vazquez,M A Herrero,Amable Linan
Publisher : CRC Press
Page : 236 pages
File Size : 48,8 Mb
Release : 1995-04-04
Category : Mathematics
ISBN : 0582256453
This research note consists of selected contributions from the 1993 International Conference on "Free Boundary Problems: Theory and Applications." These represent coherent and high-level research in the field of free boundary problems. Topics include mean curvature flows, phase transitions and material sciences, fluid mechanics and combustion problems.
Author : Antonio Fasano,Mario Primicerio
Publisher : Pitman Advanced Publishing Program
Page : 346 pages
File Size : 48,9 Mb
Release : 1983
Category : Boundary value problems
ISBN : UCSD:31822008735268
Author : Arshak Petrosyan,Henrik Shahgholian,Nina Nikolaevna Uralʹt︠s︡eva
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 51,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821887943
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 : Darya Apushkinskaya
Publisher : Springer
Page : 146 pages
File Size : 42,7 Mb
Release : 2018-09-20
Category : Mathematics
ISBN : 9783319970790
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 : Donatella Danielli,Arshak Petrosyan,Camelia A. Pop
Publisher : American Mathematical Soc.
Page : 214 pages
File Size : 40,8 Mb
Release : 2019-02-21
Category : Differential equations
ISBN : 9781470441104
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 : Vladimir Gutlyanskii,Vladimir Ryazanov,Uri Srebro,Eduard Yakubov
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 44,9 Mb
Release : 2012-04-23
Category : Mathematics
ISBN : 9781461431916
This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics. The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behavior of solutions to the Beltrami equations. The monograph contains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary. The most important feature of this book concerns the unified geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations. Mastering and using these new tools also gives essential advantages for the reader in the research of modern problems in many other domains. Every mathematics graduate library should have a copy of this book.
Author : C.M. Dafermos,Milan Pokorny
Publisher : Elsevier
Page : 609 pages
File Size : 52,7 Mb
Release : 2008-10-06
Category : Mathematics
ISBN : 9780080931975
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts
Author : Pierluigi Colli,Claudio Verdi,Augusto Visintin
Publisher : Birkhäuser
Page : 342 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878937
Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary". A further quantitative condition is then provided in order to exclude indeterminacy. Free boundary problems thus encompass a broad spectrum which is represented in this state-of-the-art volume by a variety of contributions of researchers in mathematics and applied fields like physics, biology and material sciences. Special emphasis has been reserved for mathematical modelling and for the formulation of new problems.
Author : Eugene Bloch,Courant Institute of Mathematical Sciences
Publisher : Unknown
Page : 123 pages
File Size : 53,9 Mb
Release : 1969
Category : Boundary value problems
ISBN : OCLC:12855025
Author : John Lewis,Peter Lindqvist,Juan J. Manfredi,Sandro Salsa
Publisher : Springer
Page : 247 pages
File Size : 50,5 Mb
Release : 2012-03-02
Category : Mathematics
ISBN : 9783642271458
The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still remains a very fruitful research field. In particular considerable strides have been made in regularity estimates for degenerate and singular elliptic and parabolic equations over the last several years, and in many unexpected and challenging directions. Because of all these recent results, it seemed high time to create an overview that would highlight emerging trends and issues in this fascinating research topic in a proper and effective way. The course aimed to show the deep connections between these topics and to open new research directions through the contributions of leading experts in all of these fields.
