Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces
Series: Springer Monographs in Mathematics;
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Product details:
- Edition number 1st ed. 2021
- Publisher Springer
- Date of Publication 3 November 2022
- Number of Volumes 1 pieces, Book
- ISBN 9783030888589
- Binding Paperback
- No. of pages389 pages
- Size 235x155 mm
- Weight 617 g
- Language English
- Illustrations XIII, 389 p. 451
Categories
Short description:
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.
MoreLong description:
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.
More
Table of Contents:
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.
Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces
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