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Partial differential equations in an...

Chlebicka, Iwona.

Partial differential equations in anisotropic musielak-orlicz spaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Partial differential equations in anisotropic musielak-orlicz spacesby Iwona Chlebicka ... [et al.].
other author:	Chlebicka, Iwona.
Published:	Cham :Springer International Publishing :2021.
Description:	xiii, 389 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Functional Analysis.
Online resource:	https://doi.org/10.1007/978-3-030-88856-5
ISBN:	9783030888565$q(electronic bk.)

Partial differential equations in anisotropic musielak-orlicz spaces
Partial differential equations in anisotropic musielak-orlicz spaces[electronic resource] /by Iwona Chlebicka ... [et al.]. - Cham :Springer International Publishing :2021. - xiii, 389 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

Part I Overture: 1. Introduction -- 2. N-Functions -- 3. Musielak-Orlicz Spaces -- Part II PDEs: 4. Weak Solutions -- 5. Renormalized Solutions -- 6. Homogenization of Elliptic Boundary Value Problems -- 7. Non-Newtonian Fluids -- Part III Auxiliaries: 8. Basics -- 9. Functional Inequalities -- References -- List of Symbols -- Index.

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.

ISBN: 9783030888565$q(electronic bk.)

Standard No.: 10.1007/978-3-030-88856-5doiSubjects--Topical Terms:

274845
Functional Analysis.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Partial differential equations in anisotropic musielak-orlicz spaces
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490 1 $a Springer monographs in mathematics, $x 2196-9922
505 0 $a Part I Overture: 1. Introduction -- 2. N-Functions -- 3. Musielak-Orlicz Spaces -- Part II PDEs: 4. Weak Solutions -- 5. Renormalized Solutions -- 6. Homogenization of Elliptic Boundary Value Problems -- 7. Non-Newtonian Fluids -- Part III Auxiliaries: 8. Basics -- 9. Functional Inequalities -- References -- List of Symbols -- Index.
520 $a 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.
650 2 4 $a Functional Analysis. $3 274845
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