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Solutions Of Elliptic Equations Involving Critical Sobolev Exponents With Neumann Boundary Conditions
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Book Synopsis Recent Advances on Elliptic and Parabolic Issues by : Michel Chipot
Download or read book Recent Advances on Elliptic and Parabolic Issues written by Michel Chipot and published by World Scientific. This book was released on 2006 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of articles discussing the most recent advances on various topics in partial differential equations. Many important issues regarding evolution problems, their asymptotic behavior and their qualitative properties are addressed. The quality and completeness of the articles will make this book a source of inspiration and references in the future. Contents: Steady Free Convection in a Bounded and Saturated Porous Medium (S Akesbi et al.); Quasilinear Parabolic Functional Evolution Equations (H Amann); A Linear Parabolic Problem with Non-Dissipative Dynamical Boundary Conditions (C Bandle & W Reichel); Remarks on Some Class of Nonlocal Elliptic Problems (M Chipot); On Some Definitions and Properties of Generalized Convex Sets Arising in the Calculus of Variations (B Dacorogna et al.); Note on the Asymptotic Behavior of Solutions to an Anisotropic Crystalline Curvature Flow (C Hirota et al.); A Reaction-Diffusion Approximation to a Cross-Diffusion System (M Iida et al.); Bifurcation Diagrams to an Elliptic Equation Involving the Critical Sobolev Exponent with the Robin Condition (Y Kabeya); Ginzburg-Landau Functional in a Thin Loop and Local Minimizers (S Kosugi & Y Morita); Singular Limit for Some Reaction Diffusion System (K Nakashima); Rayleigh-B(r)nard Convection in a Rectangular Domain (T Ogawa & T Okuda); Some Convergence Results for Elliptic Problems with Periodic Data (Y Xie); On Global Unbounded Solutions for a Semilinear Parabolic Equation (E Yanagida). Readership: Graduate students and researchers in partial differential equations and nonlinear science.
Book Synopsis World Congress of Nonlinear Analysts '92 by : V. Lakshmikantham
Download or read book World Congress of Nonlinear Analysts '92 written by V. Lakshmikantham and published by Walter de Gruyter. This book was released on 2011-11-14 with total page 4040 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Recent Advances On Elliptic And Parabolic Issues - Proceedings Of The 2004 Swiss-japanese Seminar by : Michel Marie Chipot
Download or read book Recent Advances On Elliptic And Parabolic Issues - Proceedings Of The 2004 Swiss-japanese Seminar written by Michel Marie Chipot and published by World Scientific. This book was released on 2006-03-01 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of articles discussing the most recent advances on various topics in partial differential equations. Many important issues regarding evolution problems, their asymptotic behavior and their qualitative properties are addressed. The quality and completeness of the articles will make this book a source of inspiration and references in the future.
Book Synopsis Handbook of Differential Equations:Stationary Partial Differential Equations by : Michel Chipot
Download or read book Handbook of Differential Equations:Stationary Partial Differential Equations written by Michel Chipot and published by Elsevier. This book was released on 2005-08-19 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of self contained, state-of-the-art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.Partial differential equations represent one of the most rapidly developing topics in mathematics. This is due to their numerous applications in science and engineering on the one hand and to the challenge and beauty of associated mathematical problems on the other.Key features:- Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.- Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.
Book Synopsis Degenerate Diffusions by : Wei-Ming Ni
Download or read book Degenerate Diffusions written by Wei-Ming Ni and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications DEGENERATE DIFFUSIONS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries". The aim of this workshop was to provide some focus in the study of degenerate diffusion equations, and by involving scientists and engineers as well as mathematicians, to keep this focus firmly linked to concrete problems. We thank Wei-Ming Ni, L.A. Peletier and J.L. Vazquez for organizing the meet ing. We especially thank Wei-Ming Ni for editing the proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, the National Science Foun dation, and the Office of Naval Research. A vner Friedman Willard Miller, Jr. PREFACE This volume is the proceedings of the IMA workshop "Degenerate Diffusions" held at the University of Minnesota from May 13 to May 18, 1991.
Book Synopsis Exploiting Symmetry in Applied and Numerical Analysis by : Eugene L. Allgower
Download or read book Exploiting Symmetry in Applied and Numerical Analysis written by Eugene L. Allgower and published by American Mathematical Soc.. This book was released on 1993 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry plays an important role in theoretical physics, applied analysis, classical differential equations, and bifurcation theory. Although numerical analysis has incorporated aspects of symmetry on an ad hoc basis, there is now a growing collection of numerical analysts who are currently attempting to use symmetry groups and representation theory as fundamental tools in their work. This book contains the proceedings of an AMS-SIAM Summer Seminar in Applied Mathematics, held in 1992 at Colorado State University. The seminar, which drew about 100 scientists from around the world, was intended to stimulate the systematic incorporation of symmetry and group theoretical concepts into numerical methods. The papers in this volume have been refereed and will not be published elsewhere.
Book Synopsis Morse Index of Solutions of Nonlinear Elliptic Equations by : Lucio Damascelli
Download or read book Morse Index of Solutions of Nonlinear Elliptic Equations written by Lucio Damascelli and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-08 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents in a unified manner the use of the Morse index, and especially its connections to the maximum principle, in the study of nonlinear elliptic equations. The knowledge or a bound on the Morse index of a solution is a very important qualitative information which can be used in several ways for different problems, in order to derive uniqueness, existence or nonexistence, symmetry, and other properties of solutions.
Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States, 3 by : N.G Lloyd
Download or read book Nonlinear Diffusion Equations and Their Equilibrium States, 3 written by N.G Lloyd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. Central to the theory is the equation Ut = ~cp(U) + f(u). Here ~ denotes the n-dimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in space-time. FUn damental questions concern the existence, uniqueness and regularity of so lutions, the existence of interfaces or free boundaries, the question as to whether or not the solution can be continued for all time, the asymptotic behavior, both in time and space, and the development of singularities, for instance when the solution ceases to exist after finite time, either through extinction or through blow up.
Book Synopsis Lebesgue and Sobolev Spaces with Variable Exponents by : Lars Diening
Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer Science & Business Media. This book was released on 2011-03-31 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
Book Synopsis The Lin-Ni's Problem for Mean Convex Domains by : Olivier Druet
Download or read book The Lin-Ni's Problem for Mean Convex Domains written by Olivier Druet and published by American Mathematical Soc.. This book was released on 2012 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a smooth bounded domain of $\mathbb{R}^n$, $n\geq 3$. In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when $n=3$ or $n\geq 7$. As a direct consequence, they prove the validity of the Lin-Ni's conjecture in dimension $n=3$ and $n\geq 7$ for mean convex domains and with bounded energy. Recent examples by Wang-Wei-Yan show that the bound on the energy is a necessary condition.
Book Synopsis Variational Methods for Nonlocal Fractional Problems by : Giovanni Molica Bisci
Download or read book Variational Methods for Nonlocal Fractional Problems written by Giovanni Molica Bisci and published by Cambridge University Press. This book was released on 2016-03-11 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.
Book Synopsis Topics in Mathematical Analysis by : Paolo Ciatti
Download or read book Topics in Mathematical Analysis written by Paolo Ciatti and published by World Scientific. This book was released on 2008 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of a series of lecture notes on mathematical analysis. The contributors have been selected on the basis of both their outstanding scientific level and their clarity of exposition. Thus, the present collection is particularly suited to young researchers and graduate students. Through this volume, the editors intend to provide the reader with material otherwise difficult to find and written in a manner which is also accessible to nonexperts.
Book Synopsis Topological Methods, Variational Methods and Their Applications by : Haim Brzis
Download or read book Topological Methods, Variational Methods and Their Applications written by Haim Brzis and published by World Scientific. This book was released on 2003 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 1418, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University. 166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrvdinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.
Book Synopsis Topological Methods, Variational Methods And Their Applications - Proceedings Of The Icm2002 Satellite Conference On Nonlinear Functional Analysis by : Haim Brezis
Download or read book Topological Methods, Variational Methods And Their Applications - Proceedings Of The Icm2002 Satellite Conference On Nonlinear Functional Analysis written by Haim Brezis and published by World Scientific. This book was released on 2003-03-13 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 14-18, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University.166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrödinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.
Download or read book Pacific Journal of Mathematics written by and published by . This book was released on 2001-10 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Recent Trends in Nonlinear Partial Differential Equations II by : James Serrin
Download or read book Recent Trends in Nonlinear Partial Differential Equations II written by James Serrin and published by American Mathematical Soc.. This book was released on 2013 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honour of Patrizia Pucci's 60th birthday. The workshop brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants.
Book Synopsis Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations by : Vicentiu D. Radulescu
Download or read book Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations written by Vicentiu D. Radulescu and published by Hindawi Publishing Corporation. This book was released on 2008 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they appear as mathematical models in different branches of physics, chemistry, biology, genetics, and engineering and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on the calculus of variations and functional analysis. Concentrating on single-valued or multivalued elliptic equations with nonlinearities of various types, the aim of this volume is to obtain sharp existence or nonexistence results, as well as decay rates for general classes of solutions. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including bifurcation, stability, asymptotic analysis, and optimal regularity of solutions. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. A systematic description of the most relevant singular phenomena described in this volume includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear phenomena described by elliptic partial differential equations.
