Obstacle Problems In Mathematical Physics

Author : J.-F. Rodrigues
Publisher : Elsevier
Page : 351 pages
File Size : 51,6 Mb
Release : 1987-03-01
Category : Science
ISBN : 008087245X

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Obstacle Problems in Mathematical Physics by J.-F. Rodrigues Pdf

The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics. The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.

Author : Arshak Petrosyan,Henrik Shahgholian,Nina Nikolaevna Uralʹt︠s︡eva
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 50,7 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 : 48,8 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 : Olʹga A. Ladyženskaja
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 53,9 Mb
Release : 1973
Category : Boundary value problems
ISBN : 0821830163

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Boundary Value Problems of Mathematical Physics by Olʹga A. Ladyženskaja Pdf

Author : M. Chipot
Publisher : Springer Science & Business Media
Page : 127 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461211204

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Variational Inequalities and Flow in Porous Media by M. Chipot Pdf

These notes are the contents of a one semester graduate course which taught at Brown University during the academic year 1981-1982. They are mainly concerned with regularity theory for obstacle problems, and with the dam problem, which, in the rectangular case, is one of the most in teresting applications of Variational Inequalities with an obstacle. Very little background is needed to read these notes. The main re sults of functional analysis which are used here are recalled in the text. The goal of the two first chapters is to introduce the notion of Varia tional Inequality and give some applications from physical mathematics. The third chapter is concerned with a regularity theory for the obstacle problems. These problems have now invaded a large domain of applied mathematics including optimal control theory and mechanics, and a collec tion of regularity results available seems to be timely. Roughly speaking, for elliptic variational inequalities of second order we prove that the solution has as much regularity as the obstacle(s). We combine here the theory for one or two obstacles in a unified way, and one of our hopes is that the reader will enjoy the wide diversity of techniques used in this approach. The fourth chapter is concerned with the dam problem. This problem has been intensively studied during the past decade (see the books of Baiocchi-Capelo and Kinderlehrer-Stampacchia in the references). The relationship with Variational Inequalities has already been quoted above.

Author : R. Carroll
Publisher : Elsevier
Page : 411 pages
File Size : 51,9 Mb
Release : 1988-06-01
Category : Science
ISBN : 9780080872636

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Mathematical Physics by R. Carroll Pdf

An introduction to the important areas of mathematical physics, this volume starts with basic ideas and proceeds (sometimes rapidly) to a more sophisticated level, often to the context of current research.All of the necessary functional analysis and differential geometry is included, along with basic calculus of variations and partial differential equations (linear and nonlinear). An introduction to classical and quantum mechanics is given with topics in Feynman integrals, gauge fields, geometric quantization, attractors for PDE, Ginzburg-Landau Equations in superconductivity, Navier-Stokes equations, soliton theory, inverse problems and ill-posed problems, scattering theory, convex analysis, variational inequalities, nonlinear semigroups, etc. Contents: 1. Classical Ideas and Problems. Introduction. Some Preliminary Variational Ideas. Various Differential Equations and Their Origins. Linear Second Order PDE. Further Topics in the Calculus of Variations. Spectral Theory for Ordinary Differential Operators, Transmutation, and Inverse Problems. Introduction to Classical Mechanics. Introduction to Quantum Mechanics. Weak Problems in PDE. Some Nonlinear PDE. Ill-Posed Problems and Regularization. 2. Scattering Theory and Solitons. Introduction. Scattering Theory I (Operator Theory). Scattering Theory II (3-D). Scattering Theory III (A Medley of Themes). Scattering Theory IV (Spectral Methods in 3-D). Systems and Half Line Problems. Relations between Potentials and Spectral Data. Introduction to Soliton Theory. Solitons via AKNS Systems. Soliton Theory (Hamiltonian Structure). Some Topics in Integrable Systems. 3. Some Nonlinear Analysis: Some Geometric Formalism. Introduction. Nonlinear Analysis. Monotone Operators. Topological Methods. Convex Analysis. Nonlinear Semigroups and Monotone Sets. Variational Inequalities. Quantum Field Theory. Gauge Fields (Physics). Gauge Fields (Mathematics) and Geometric Quantization. Appendices: Introduction to Linear Functional Analysis. Selected Topics in Functional Analysis. Introduction to Differential Geometry. References. Index.

Author : Vladimir Gavrilovich Romanov
Publisher : BRILL
Page : 260 pages
File Size : 52,8 Mb
Release : 1987
Category : Mathematics
ISBN : 9067640565

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Inverse Problems of Mathematical Physics by Vladimir Gavrilovich Romanov Pdf

Author : Olga Alexandrovna Ladyzhenskaya
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 51,8 Mb
Release : 1977
Category : Boundary value problems
ISBN : 0821830279

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Boundary Value Problems of Mathematical Physics. IX by Olga Alexandrovna Ladyzhenskaya Pdf

Author : Carles Casacuberta,Rosa M. Miro-Roig,Joan Verdera,Sebastia Xambo-Descamps
Publisher : Birkhäuser
Page : 630 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882668

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European Congress of Mathematics by Carles Casacuberta,Rosa M. Miro-Roig,Joan Verdera,Sebastia Xambo-Descamps Pdf

This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.

Author : Yulia E. Karpeshina,Günter Stolz,Rudi Weikard,Yanni Zeng
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 46,5 Mb
Release : 2003
Category : Differential equations
ISBN : 9780821832967

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Advances in Differential Equations and Mathematical Physics by Yulia E. Karpeshina,Günter Stolz,Rudi Weikard,Yanni Zeng Pdf

This volume presents the proceedings of the 9th International Conference on Differential Equations and Mathematical Physics. It contains 29 research and survey papers contributed by conference participants. The conference provided researchers a forum to present and discuss their recent results in a broad range of areas encompassing the theory of differential equations and their applications in mathematical physics. Papers in this volume represent some of the most interesting results and the major areas of research that were covered, including spectral theory with applications to non-relativistic and relativistic quantum mechanics, including time-dependent and random potential, resonances, many body systems, pseudodifferential operators and quantum dynamics, inverse spectral and scattering problems, the theory of linear and nonlinear partial differential equations with applications in fluid dynamics, conservation laws and numerical simulations, as well as equilibrium and nonequilibrium statistical mechanics. The volume is intended for graduate students and researchers interested in mathematical physics.

Author : Darya Apushkinskaya
Publisher : Springer
Page : 146 pages
File Size : 40,7 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 : Boris Mikha?lovich Budak,Aleksandr Andreevich Samarski?,Andre? Nikolaevich Tikhonov
Publisher : Courier Corporation
Page : 802 pages
File Size : 51,9 Mb
Release : 1964-01-01
Category : Science
ISBN : 9780486658063

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A Collection of Problems in Mathematical Physics by Boris Mikha?lovich Budak,Aleksandr Andreevich Samarski?,Andre? Nikolaevich Tikhonov Pdf

Outstanding, wide-ranging material on classification and reduction to canonical form of second-order differential equations; hyperbolic, parabolic, elliptic equations, more. Bibliography.

Author : Gaurav Gupta,Lipo Wang,Anupam Yadav,Puneet Rana,Zhenyu Wang
Publisher : Springer Nature
Page : 415 pages
File Size : 49,8 Mb
Release : 2022-02-01
Category : Technology & Engineering
ISBN : 9789811668876

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Proceedings of Academia-Industry Consortium for Data Science by Gaurav Gupta,Lipo Wang,Anupam Yadav,Puneet Rana,Zhenyu Wang Pdf

This book gathers high-quality papers presented at Academia-Industry Consortium for Data Science (AICDS 2020), held in Wenzhou, China during 19 – 20 December 2020. The book presents views of academicians and also how companies are approaching these challenges organizationally. The topics covered in the book are data science and analytics, natural language processing, predictive analytics, artificial intelligence, machine learning, deep learning, big data computing, cognitive computing, data visualization, image processing, and optimization techniques.

Author : O. A. Ladyzhenskaya,O. A. Ladyzhenskaëiìa
Publisher : American Mathematical Soc.
Page : 239 pages
File Size : 45,8 Mb
Release : 1991
Category : Mathematics
ISBN : 0821831410

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Boundary Value Problems of Mathematical Physics by O. A. Ladyzhenskaya,O. A. Ladyzhenskaëiìa Pdf

Author : Michael C. Ferris,Jong-Shi Pang
Publisher : SIAM
Page : 494 pages
File Size : 41,6 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 0898713919

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Complementarity and Variational Problems by Michael C. Ferris,Jong-Shi Pang Pdf

After more than three decades of research, the subject of complementarity problems and its numerous extensions has become a well-established and fruitful discipline within mathematical programming and applied mathematics. Sources of these problems are diverse and span numerous areas in engineering, economics, and the sciences. Includes refereed articles.