Partial differential equations in anisotropic Musielak-Orlicz spaces [electronic resource] / Iwona Chlebicka, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Aneta Wróblewska-Kamińskas.

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Partial differential equations in anisotropic Musielak-Orlicz spaces [electronic resource] / Iwona Chlebicka, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Aneta Wróblewska-Kamińskas.

9783030888565 (electronic bk.)
3030888568 (electronic bk.)
303088855X
9783030888558

Cham, Switzerland : Springer, 2021.

English

1 online resource.

10.1007/978-3-030-88856-5 doi

QA377

515/.353

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 MusielakOrlicz 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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed November 12, 2021).

Springer monographs in mathematics.

Print version: 9783030888558

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