Nonlinear Elliptic Equations of the Second Order, Qing Han

Автор: Lopez Gomez Julian
Название: Linear Second Order Elliptic Operators
ISBN: 9814440248 ISBN-13(EAN): 9789814440240
Издательство: World Scientific Publishing
Цена: 48570.00 T
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Описание: The main goal of the book is to provide a comprehensive and self-contained proof of the, relatively recent, theorem of characterization of the strong maximum principle due to Molina-Meyer and the author, published in Diff. Int. Eqns. in 1994, which was later refined by Amann and the author in a paper published in J. of Diff. Eqns. in 1998. Besides this characterization has been shown to be a pivotal result for the development of the modern theory of spatially heterogeneous nonlinear elliptic and parabolic problems; it has allowed us to update the classical theory on the maximum and minimum principles by providing with some extremely sharp refinements of the classical results of Hopf and Protter-Weinberger. By a celebrated result of Berestycki, Nirenberg and Varadhan, Comm. Pure Appl. Maths. in 1994, the characterization theorem is partially true under no regularity constraints on the support domain for Dirichlet boundary conditions.Instead of encyclopedic generality, this book pays special attention to completeness, clarity and transparency of its exposition so that it can be taught even at an advanced undergraduate level. Adopting this perspective, it is a textbook; however, it is simultaneously a research monograph about the maximum principle, as it brings together for the first time in the form of a book, the most paradigmatic classical results together with a series of recent fundamental results scattered in a number of independent papers by the author of this book and his collaborators.Chapters 3, 4, and 5 can be delivered as a classical undergraduate, or graduate, course in Hilbert space techniques for linear second order elliptic operators, and Chaps. 1 and 2 complete the classical results on the minimum principle covered by the paradigmatic textbook of Protter and Weinberger by incorporating some recent classification theorems of supersolutions by Walter, 1989, and the author, 2003. Consequently, these five chapters can be taught at an undergraduate, or graduate, level. Chapters 6 and 7 study the celebrated theorem of Krein-Rutman and infer from it the characterizations of the strong maximum principle of Molina-Meyer and Amann, in collaboration with the author, which have been incorporated to a textbook by the first time here, as well as the results of Chaps. 8 and 9, polishing some recent joint work of Cano-Casanova with the author. Consequently, the second half of the book consists of a more specialized monograph on the maximum principle and the underlying principal eigenvalues.

Автор: Pao, C. V.
Название: Nonlinear parabolic and elliptic equations
ISBN: 1461363233 ISBN-13(EAN): 9781461363231
Издательство: Springer
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Цена: 158380.00 T
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Описание: In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.

Автор: Ilya J. Bakelman
Название: Convex Analysis and Nonlinear Geometric Elliptic Equations
ISBN: 3642698832 ISBN-13(EAN): 9783642698835
Издательство: Springer
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Цена: 79190.00 T
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Описание: Investigations in modem nonlinear analysis rely on ideas, methods and prob- lems from various fields of mathematics, mechanics, physics and other applied sciences.

Автор: Wazwaz Abdul-Majid
Название: First Course In Integral Equations, A (Second Edition)
ISBN: 9814675121 ISBN-13(EAN): 9789814675123
Издательство: World Scientific Publishing
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Цена: 42240.00 T
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Описание: This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations.

Автор: Ahmad Shair
Название: Textbook on Ordinary Differential Equations
ISBN: 3319164074 ISBN-13(EAN): 9783319164076
Издательство: Springer
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Цена: 46570.00 T
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Описание: The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available.

Автор: Dret, Herve Le
Название: Nonlinear elliptic partial differential equations
ISBN: 3319783890 ISBN-13(EAN): 9783319783895
Издательство: Springer
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Цена: 60550.00 T
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Описание: 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.

Автор: Ariel Barton, Svitlana Mayboroda
Название: Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces
ISBN: 1470419890 ISBN-13(EAN): 9781470419899
Издательство: Mare Nostrum (Eurospan)
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Цена: 83160.00 T
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Описание: Presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable $t$-independent coefficients in spaces of fractional smoothness, in Besov and weighted $L^p$ classes. In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.

Автор: N.V. Krylov
Название: Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations
ISBN: 1470447401 ISBN-13(EAN): 9781470447403
Издательство: Mare Nostrum (Eurospan)
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Цена: 107850.00 T
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Описание: This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov-Safonov and the Evans-Krylov theorems, are taken from old sources, and the main results were obtained in the last few years.Presentation of these results is based on a generalization of the Fefferman-Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called ``ersatz'' existence theorems, saying that one can slightly modify ``any'' equation and get a ``cut-off'' equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.

Автор: Agmon Shmuel
Название: Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operations. (MN-29)
ISBN: 0691613672 ISBN-13(EAN): 9780691613673
Издательство: Wiley
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Цена: 31680.00 T
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Описание: Mathematical Notes, 29 Originally published in 1983. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paper

Автор: Abdelhamid Meziani
Название: On First and Second Order Planar Elliptic Equations with Degeneracies
ISBN: 0821853120 ISBN-13(EAN): 9780821853122
Издательство: Mare Nostrum (Eurospan)
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Цена: 60060.00 T
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Описание: "May 2012, volume 217, number 1019 (first of 4 numbers)."

Автор: Alexander A. Kovalevsky, Igor I. Skrypnik, Andrey E. Shishkov
Название: Singular Solutions of Nonlinear Elliptic and Parabolic Equations
ISBN: 3110315483 ISBN-13(EAN): 9783110315486
Издательство: Walter de Gruyter
Цена: 223090.00 T
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Описание: This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form.The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis.Contents:ForewordPart I: Nonlinear elliptic equations with L^1-dataNonlinear elliptic equations of the second order with L^1-dataNonlinear equations of the fourth order with strengthened coercivity and L^1-dataPart II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second orderRemovability of singularities of the solutions of quasilinear elliptic equationsRemovability of singularities of the solutions of quasilinear parabolic equationsQuasilinear elliptic equations with coefficients from the Kato classPart III: Boundary regimes with peaking for quasilinear parabolic equationsEnergy methods for the investigation of localized regimes with peaking for parabolic second-order equationsMethod of functional inequalities in peaking regimes for parabolic equations of higher ordersNonlocalized regimes with singular peakingAppendix: Formulations and proofs of the auxiliary resultsBibliography