Download or read book Regularity Results for Nonlinear Elliptic Systems and Applications written by Alain Bensoussan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects many helpful techniques for obtaining regularity results for solutions of nonlinear systems of partial differential equations. These are applied in various cases to provide useful examples and relevant results, particularly in such fields as fluid mechanics, solid mechanics, semiconductor theory and game theory.
Download or read book Regularity Results for Nonlinear Elliptic Systems and Applications written by Alain Bensoussan and published by . This book was released on 2014-01-15 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Regularity Theory for Nonlinear Elliptic Systems written by Mariano Giaquinta and published by Birkhauser. This book was released on 1993 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Functional Analysis and Its Applications Part 2 written by Felix E. Browder and published by American Mathematical Soc.. This book was released on 1986 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to the Regularity Theory for Nonlinear Elliptic Systems written by Mariano Giaquinta and published by . This book was released on 1984 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to the Regularity Theory for Elliptic Systems Harmonic Maps and Minimal Graphs written by Mariano Giaquinta and published by Springer Science & Business Media. This book was released on 2013-07-30 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certain assumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to as regularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of the basic ideas and techniques introduced in this context, confining ourselves to important but simple situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, direct methods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and L^p-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar case and partial regularity theorems in the vector valued case; energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensional weakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of the L^p theory, including the celebrated results of Wente and of Coifman-Lions-Meyer-Semmes.
Download or read book Numerical Methods for Nonlinear Elliptic Differential Equations written by Klaus Böhmer and published by Oxford University Press. This book was released on 2010-10-07 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boehmer systmatically handles the different numerical methods for nonlinear elliptic problems.
Download or read book Direct Methods in the Theory of Elliptic Equations written by Jindrich Necas and published by Springer Science & Business Media. This book was released on 2011-10-06 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nečas’ book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition, translated by G. Tronel and A. Kufner, presents Nečas’ work essentially in the form it was published in 1967. It gives a timeless and in some sense definitive treatment of a number issues in variational methods for elliptic systems and higher order equations. The text is recommended to graduate students of partial differential equations, postdoctoral associates in Analysis, and scientists working with linear elliptic systems. In fact, any researcher using the theory of elliptic systems will benefit from having the book in his library. The volume gives a self-contained presentation of the elliptic theory based on the "direct method", also known as the variational method. Due to its universality and close connections to numerical approximations, the variational method has become one of the most important approaches to the elliptic theory. The method does not rely on the maximum principle or other special properties of the scalar second order elliptic equations, and it is ideally suited for handling systems of equations of arbitrary order. The prototypical examples of equations covered by the theory are, in addition to the standard Laplace equation, Lame’s system of linear elasticity and the biharmonic equation (both with variable coefficients, of course). General ellipticity conditions are discussed and most of the natural boundary condition is covered. The necessary foundations of the function space theory are explained along the way, in an arguably optimal manner. The standard boundary regularity requirement on the domains is the Lipschitz continuity of the boundary, which "when going beyond the scalar equations of second order" turns out to be a very natural class. These choices reflect the author's opinion that the Lame system and the biharmonic equations are just as important as the Laplace equation, and that the class of the domains with the Lipschitz continuous boundary (as opposed to smooth domains) is the most natural class of domains to consider in connection with these equations and their applications.
Download or read book Methods on Nonlinear Elliptic Equations written by Wenxiong Chen and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book IUTAM Symposium on Theoretical Computational and Modelling Aspects of Inelastic Media written by B. Daya Reddy and published by Springer Science & Business Media. This book was released on 2008-09-24 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work comprises papers based on some of the talks presented at the IUTAM Symposium of the same name, held in Cape Town, January 14-18, 2008. This volume treats cutting-edge issues in modelling, the behaviour of various classes of inelastic media, and associated algorithms for carrying out computational simulations. A key feature of the contributions are works directed at modelling behaviour at the meso and micro-scales, and at bridging the micro-macro scales.
Download or read book Elliptic Regularity Theory written by Lisa Beck and published by Springer. This book was released on 2016-04-08 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed. Finally, a short overview is given on the current state of the art concerning the size of the singular set on which discontinuities may occur. The notes are intended for graduate and postgraduate students with a solid background in functional analysis and some familiarity with partial differential equations; they will also be of interest to researchers working on related topics.
Download or read book Cross Diffusion Systems written by Dung Le and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-10-24 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new findings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenberg inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.
Download or read book Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems AM 105 Volume 105 written by Mariano Giaquinta and published by Princeton University Press. This book was released on 2016-03-02 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forthcoming.
Download or read book Optimization of Elliptic Systems written by Pekka Neittaanmaki and published by Springer Science & Business Media. This book was released on 2007-01-04 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau [1984], Haslinger and Neittaanmaki [1988], [1996], Sokolowski and Zolksio [1992], Litvinov [2000], Allaire [2001], Mohammadi and Pironneau [2001], Delfour and Zolksio [2001], and Makinen and Haslinger [2003]. Already Lions [I9681 devoted a major part of his classical monograph on the optimal control of partial differential equations to the optimization of elliptic systems. Let us also mention that even the very first known problem of the calculus of variations, the brachistochrone studied by Bernoulli back in 1696. is in fact a shape optimization problem. The natural richness of this mathematical research subject, as well as the extremely large field of possible applications, has created the unusual situation that although many important results and methods have already been est- lished, there are still pressing unsolved questions. In this monograph, we aim to address some of these open problems; as a consequence, there is only a minor overlap with the textbooks already existing in the field.
Download or read book The Energy Method Stability and Nonlinear Convection written by brian straughan and published by Springer Science & Business Media. This book was released on 2003-10-01 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Six new chapters (14-19) deal with topics of current interest: multi-component convection diffusion, convection in a compressible fluid, convenction with temperature dependent viscosity and thermal conductivity, penetrative convection, nonlinear stability in ocean circulation models, and numerical solution of eigenvalue problems.
Download or read book The Regularity of General Parabolic Systems with Degenerate Diffusion written by Verena Bögelein and published by American Mathematical Soc.. This book was released on 2013-01-28 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the paper is twofold. On one hand the authors want to present a new technique called $p$-caloric approximation, which is a proper generalization of the classical compactness methods first developed by DeGiorgi with his Harmonic Approximation Lemma. This last result, initially introduced in the setting of Geometric Measure Theory to prove the regularity of minimal surfaces, is nowadays a classical tool to prove linearization and regularity results for vectorial problems. Here the authors develop a very far reaching version of this general principle devised to linearize general degenerate parabolic systems. The use of this result in turn allows the authors to achieve the subsequent and main aim of the paper, that is, the implementation of a partial regularity theory for parabolic systems with degenerate diffusion of the type $\partial_t u - \mathrm{div} a(Du)=0$, without necessarily assuming a quasi-diagonal structure, i.e. a structure prescribing that the gradient non-linearities depend only on the the explicit scalar quantity.
Download or read book Mean Field Games and Mean Field Type Control Theory written by Alain Bensoussan and published by Springer Science & Business Media. This book was released on 2013-10-16 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem.
