Partial Differential Equations In Anisotropic Musielak Orlicz Spaces
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Partial Differential Equations In Anisotropic Musielak Orlicz Spaces
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Author : Iwona Chlebicka
language : en
Publisher:
Release Date : 2021
Partial Differential Equations In Anisotropic Musielak Orlicz Spaces written by Iwona Chlebicka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with 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.
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.
Orlicz Spaces And Generalized Orlicz Spaces
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Author : Petteri Harjulehto
language : en
Publisher: Springer
Release Date : 2019-05-07
Orlicz Spaces And Generalized Orlicz Spaces written by Petteri Harjulehto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.
This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–Poincaré inequalities in norm and modular forms. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.
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
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
Real Variable Theory Of Musielak Orlicz Hardy Spaces
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Author : Dachun Yang
language : en
Publisher: Springer
Release Date : 2017-05-09
Real Variable Theory Of Musielak Orlicz Hardy Spaces written by Dachun Yang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-09 with Mathematics categories.
The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak–Orlicz Hardy-type function spaces, and to lay the foundations for further applications. The real-variable theory of function spaces has always been at the core of harmonic analysis. Recently, motivated by certain questions in analysis, some more general Musielak–Orlicz Hardy-type function spaces were introduced. These spaces are defined via growth functions which may vary in both the spatial variable and the growth variable. By selecting special growth functions, the resulting spaces may have subtler and finer structures, which are necessary in order to solve various endpoint or sharp problems. This book is written for graduate students and researchers interested in function spaces and, in particular, Hardy-type spaces.
Evolution Pdes With Nonstandard Growth Conditions
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Author : Stanislav Antontsev
language : en
Publisher: Springer
Release Date : 2015-04-01
Evolution Pdes With Nonstandard Growth Conditions written by Stanislav Antontsev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-01 with Mathematics categories.
This monograph offers the reader a treatment of the theory of evolution PDEs with nonstandard growth conditions. This class includes parabolic and hyperbolic equations with variable or anisotropic nonlinear structure. We develop methods for the study of such equations and present a detailed account of recent results. An overview of other approaches to the study of PDEs of this kind is provided. The presentation is focused on the issues of existence and uniqueness of solutions in appropriate function spaces and on the study of the specific qualitative properties of solutions, such as localization in space and time, extinction in a finite time and blow-up, or nonexistence of global in time solutions. Special attention is paid to the study of the properties intrinsic to solutions of equations with nonstandard growth.
Differential Equations Mathematical Physics And Applications Selim Grigorievich Krein Centennial
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Author : Peter Kuchment
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-07-22
Differential Equations Mathematical Physics And Applications Selim Grigorievich Krein Centennial written by Peter Kuchment and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-22 with Mathematics categories.
This is the second of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 733. Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union. The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in ordinary and partial differential equations, fluid dynamics, and various applications.
Seminar Of Mathematical Analysis
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Author : Genaro (ed.) L"pez Acedo
language : en
Publisher: Universidad de Sevilla
Release Date : 2003
Seminar Of Mathematical Analysis written by Genaro (ed.) L"pez Acedo and has been published by Universidad de Sevilla this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Ponencias de los seminarios de análisis matemáticos impartidos en Málaga y Sevilla entre septiembre de 2002 y febrero de 2003. Entre los diversos artículos que contiene citamos: Continuous descent methods, Algebras of analytic functions on Banach Spaces; también en español como Estimaciones con peso deducidas del Principio de Calderón-Zygmund, etc.
Morrey Spaces
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Author : Yoshihiro Sawano
language : en
Publisher: CRC Press
Release Date : 2020-09-16
Morrey Spaces written by Yoshihiro Sawano and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-16 with Mathematics categories.
Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding