Methods on Nonlinear Elliptic Equations

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Release : 2010
Genre : Differential equations, Elliptic
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Book Rating : 062/5 ( reviews)

Methods on Nonlinear Elliptic Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods on Nonlinear Elliptic Equations write by Wenxiong Chen. This book was released on 2010. Methods on Nonlinear Elliptic Equations available in PDF, EPUB and Kindle.

Nonlinear Elliptic Equations of the Second Order

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Release : 2016-04-15
Genre : Mathematics
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Book Rating : 072/5 ( reviews)

Nonlinear Elliptic Equations of the Second Order - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Elliptic Equations of the Second Order write by Qing Han. This book was released on 2016-04-15. Nonlinear Elliptic Equations of the Second Order available in PDF, EPUB and Kindle. Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler–Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge–Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and “elementary” proofs for results in important special cases. This book will serve as a valuable resource for graduate students or anyone interested in this subject.

Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations

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Release : 2008
Genre : Differential equations, Elliptic
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Book Rating : 395/5 ( reviews)

Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations write by Vicentiu D. Radulescu. This book was released on 2008. Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations available in PDF, EPUB and Kindle. 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.

Nonlinear Elliptic Partial Differential Equations

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Release : 2018-05-25
Genre : Mathematics
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Book Rating : 904/5 ( reviews)

Nonlinear Elliptic Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Elliptic Partial Differential Equations write by Hervé Le Dret. This book was released on 2018-05-25. Nonlinear Elliptic Partial Differential Equations available in PDF, EPUB and Kindle. This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.

Direct Methods in the Theory of Elliptic Equations

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Release : 2011-10-06
Genre : Mathematics
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Book Rating : 55X/5 ( reviews)

Direct Methods in the Theory of Elliptic Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Direct Methods in the Theory of Elliptic Equations write by Jindrich Necas. This book was released on 2011-10-06. Direct Methods in the Theory of Elliptic Equations available in PDF, EPUB and Kindle. 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.