Partial Differential Equations With Variable Exponents
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Partial Differential Equations With Variable Exponents
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Author : Vicentiu D. Radulescu
language : en
Publisher: CRC Press
Release Date : 2015-06-24
Partial Differential Equations With Variable Exponents written by Vicentiu D. Radulescu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-24 with Mathematics categories.
Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational
Partial Differential Equations With Variable Exponents
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Author : Vicentiu D. Radulescu
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2015-06-24
Partial Differential Equations With Variable Exponents written by Vicentiu D. Radulescu and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-24 with Mathematics categories.
Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear elliptic equations as well as their applications to various processes arising in the applied sciences. The analysis developed in the book is based on the notion of a generalized or weak solution. This approach leads not only to the fundamental results of existence and multiplicity of weak solutions but also to several qualitative properties, including spectral analysis, bifurcation, and asymptotic analysis. The book examines the equations from different points of view while using the calculus of variations as the unifying theme. Readers will see how all of these diverse topics are connected to other important parts of mathematics, including topology, differential geometry, mathematical physics, and potential theory.
Lebesgue And Sobolev Spaces With Variable Exponents
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Author : Lars Diening
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-31
Lebesgue And Sobolev Spaces With Variable Exponents written by Lars Diening and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-31 with Mathematics categories.
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.
Handbook Of Differential Equations Stationary Partial Differential Equations
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Author : Michel Chipot
language : en
Publisher: Elsevier
Release Date : 2006-08-08
Handbook Of Differential Equations Stationary Partial Differential Equations written by Michel Chipot and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-08 with Mathematics categories.
This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics.Key features: - Written by well-known experts in the field- Self-contained volume in series covering one of the most rapid developing topics in mathematics- Written by well-known experts in the field- Self-contained volume in series covering one of the most rapid developing topics in mathematics
Nonlinear Problems With Lack Of Compactness
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Author : Giovanni Molica Bisci
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-02-08
Nonlinear Problems With Lack Of Compactness written by Giovanni Molica Bisci and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-08 with Mathematics categories.
This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.
Optimization And Differentiation
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Author : Simon Serovajsky
language : en
Publisher: CRC Press
Release Date : 2017-09-13
Optimization And Differentiation written by Simon Serovajsky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-13 with Mathematics categories.
Optimization and Differentiation is an introduction to the application of optimization control theory to systems described by nonlinear partial differential equations. As well as offering a useful reference work for researchers in these fields, it is also suitable for graduate students of optimal control theory.
Willmore Energy And Willmore Conjecture
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Author : Magdalena D. Toda
language : en
Publisher: CRC Press
Release Date : 2017-10-30
Willmore Energy And Willmore Conjecture written by Magdalena D. Toda and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-30 with Mathematics categories.
This book is the first monograph dedicated entirely to Willmore energy and Willmore surfaces as contemporary topics in differential geometry. While it focuses on Willmore energy and related conjectures, it also sits at the intersection between integrable systems, harmonic maps, Lie groups, calculus of variations, geometric analysis and applied differential geometry. Rather than reproducing published results, it presents new directions, developments and open problems. It addresses questions like: What is new in Willmore theory? Are there any new Willmore conjectures and open problems? What are the contemporary applications of Willmore surfaces? As well as mathematicians and physicists, this book is a useful tool for postdoctoral researchers and advanced graduate students working in this area.
Variational Hemivariational Inequalities With Applications
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Author : Mircea Sofonea
language : en
Publisher: CRC Press
Release Date : 2017-10-23
Variational Hemivariational Inequalities With Applications written by Mircea Sofonea and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-23 with Mathematics categories.
This research monograph represents an outcome of the cross-fertilization between nonlinear functional analysis and mathematical modelling, and demonstrates its application to solid and contact mechanics. Based on authors’ original results, it introduces a general fixed point principle and its application to various nonlinear problems in analysis and mechanics. The classes of history-dependent operators and almost history-dependent operators are exposed in a large generality. A systematic and unified presentation contains a carefully-selected collection of new results on variational-hemivariational inequalities with or without unilateral constraints. A wide spectrum of static, quasistatic, dynamic contact problems for elastic, viscoelastic and viscoplastic materials illustrates the applicability of these theoretical results. Written for mathematicians, applied mathematicians, engineers and scientists, it is also a valuable tool for graduate students and researchers in nonlinear analysis, mathematical modelling, mechanics of solids, and contact mechanics.
Integration And Cubature Methods
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Author : Willi Freeden
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Integration And Cubature Methods written by Willi Freeden and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
In industry and economics, the most common solutions of partial differential equations involving multivariate numerical integration over cuboids include techniques of iterated one-dimensional approximate integration. In geosciences, however, the integrals are extended over potato-like volumes (such as the ball, ellipsoid, geoid, or the Earth) and their boundary surfaces which require specific multi-variate approximate integration methods. Integration and Cubature Methods: A Geomathematically Oriented Course provides a basic foundation for students, researchers, and practitioners interested in precisely these areas, as well as breaking new ground in integration and cubature in geomathematics.
Partial Differential Equations In Anisotropic Musielak Orlicz Spaces
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Author : Iwona Chlebicka
language : en
Publisher: Springer Nature
Release Date : 2021-11-01
Partial Differential Equations In Anisotropic Musielak Orlicz Spaces written by Iwona Chlebicka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-01 with Mathematics categories.
This book provides a detailed study of nonlinear partial differential equations satisfying certain nonstandard growth conditions which simultaneously extend polynomial, inhomogeneous and fully anisotropic growth. The common property of the many different kinds of equations considered is that the growth conditions of the highest order operators lead to a formulation of the equations in Musielak–Orlicz spaces. This high level of generality, understood as full anisotropy and inhomogeneity, requires new proof concepts and a generalization of the formalism, calling for an extended functional analytic framework. This theory is established in the first part of the book, which serves as an introduction to the subject, but is also an important ingredient of the whole story. The second part uses these theoretical tools for various types of PDEs, including abstract and parabolic equations but also PDEs arising from fluid and solid mechanics. For connoisseurs, there is a short chapter on homogenization of elliptic PDEs. The book will be of interest to researchers working in PDEs and in functional analysis.