Nonlinear Variational Problems And Partial Differential Equations
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Author | : A Marino |
Publisher | : CRC Press |
Total Pages | : 316 |
Release | : 1995-02-27 |
Genre | : Mathematics |
ISBN | : 9780582234369 |
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Contains proceedings of a conference held in Italy in late 1990 dedicated to discussing problems and recent progress in different aspects of nonlinear analysis such as critical point theory, global analysis, nonlinear evolution equations, hyperbolic problems, conservation laws, fluid mechanics, gamma-convergence, homogenization and relaxation methods, Hamilton-Jacobi equations, and nonlinear elliptic and parabolic systems. Also discussed are applications to some questions in differential geometry, and nonlinear partial differential equations.
Author | : Michael Struwe |
Publisher | : Springer Science & Business Media |
Total Pages | : 288 |
Release | : 2013-04-17 |
Genre | : Science |
ISBN | : 3662032120 |
Download Variational Methods Book in PDF, Epub and Kindle
Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radò. The book gives a concise introduction to variational methods and presents an overview of areas of current research in this field. This new edition has been substantially enlarged, a new chapter on the Yamabe problem has been added and the references have been updated. All topics are illustrated by carefully chosen examples, representing the current state of the art in their field.
Author | : A. Marino |
Publisher | : Longman Scientific and Technical |
Total Pages | : 236 |
Release | : 1989 |
Genre | : Mathematics |
ISBN | : |
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Author | : A. Marino |
Publisher | : Pitman Advanced Publishing Program |
Total Pages | : 144 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : |
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Author | : Dumitru Motreanu |
Publisher | : Springer Science & Business Media |
Total Pages | : 400 |
Release | : 2003-05-31 |
Genre | : Mathematics |
ISBN | : 9781402013850 |
Download Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems Book in PDF, Epub and Kindle
This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.
Author | : Martin F. Bach |
Publisher | : Birkhäuser |
Total Pages | : 162 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 303488687X |
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This self-contained research monograph focuses on semilinear Dirichlet problems and similar equations involving the p-Laplacian. The author explains new techniques in detail, and derives several numerical methods approximating the concentration point and the free boundary. The corresponding plots are highlights of this book.
Author | : Michael Struwe |
Publisher | : Springer Science & Business Media |
Total Pages | : 320 |
Release | : 2008-11-05 |
Genre | : Science |
ISBN | : 3540740139 |
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This, the fourth edition of Stuwe’s book on the calculus of variations, surveys new developments in this exciting field. It also gives a concise introduction to variational methods. In particular it includes the proof for the convergence of the Yamabe flow and a detailed treatment of the phenomenon of blow-up. Recently discovered results for backward bubbling in the heat flow for harmonic maps or surfaces are discussed. A number of changes have been made throughout the text.
Author | : Michael Struwe |
Publisher | : Springer Science & Business Media |
Total Pages | : 256 |
Release | : 2013-04-17 |
Genre | : Science |
ISBN | : 3662026244 |
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It would be hopeless to attempt to give a complete account of the history of the calculus of variations. The interest of Greek philosophers in isoperimetric problems underscores the importance of "optimal form" in ancient cultures, see Hildebrandt-Tromba [1] for a beautiful treatise of this subject. While variatio nal problems thus are part of our classical cultural heritage, the first modern treatment of a variational problem is attributed to Fermat (see Goldstine [1; p.l]). Postulating that light follows a path of least possible time, in 1662 Fer mat was able to derive the laws of refraction, thereby using methods which may already be termed analytic. With the development of the Calculus by Newton and Leibniz, the basis was laid for a more systematic development of the calculus of variations. The brothers Johann and Jakob Bernoulli and Johann's student Leonhard Euler, all from the city of Basel in Switzerland, were to become the "founding fathers" (Hildebrandt-Tromba [1; p.21]) of this new discipline. In 1743 Euler [1] sub mitted "A method for finding curves enjoying certain maximum or minimum properties", published 1744, the first textbook on the calculus of variations.
Author | : BERESTYCKI |
Publisher | : Springer Science & Business Media |
Total Pages | : 468 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1475710801 |
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In the framework of the "Annee non lineaire" (the special nonlinear year) sponsored by the C.N.R.S. (the French National Center for Scien tific Research), a meeting was held in Paris in June 1988. It took place in the Conference Hall of the Ministere de la Recherche and had as an organizing theme the topic of "Variational Problems." Nonlinear analysis has been one of the leading themes in mathemat ical research for the past decade. The use of direct variational methods has been particularly successful in understanding problems arising from physics and geometry. The growth of nonlinear analysis is largely due to the wealth of ap plications from various domains of sciences and industrial applica tions. Most of the papers gathered in this volume have their origin in applications: from mechanics, the study of Hamiltonian systems, from physics, from the recent mathematical theory of liquid crystals, from geometry, relativity, etc. Clearly, no single volume could pretend to cover the whole scope of nonlinear variational problems. We have chosen to concentrate on three main aspects of these problems, organizing them roughly around the following topics: 1. Variational methods in partial differential equations in mathemat ical physics 2. Variational problems in geometry 3. Hamiltonian systems and related topics.
Author | : Dimitrios C. Kravvaritis |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 384 |
Release | : 2020-04-06 |
Genre | : Mathematics |
ISBN | : 3110647451 |
Download Variational Methods in Nonlinear Analysis Book in PDF, Epub and Kindle
This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.