Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces (Springer Monographs in Mathematics)

Book Details:

• Author: Iwona Chlebicka

• Publisher: Springer

• Edition: 1st ed. 2021

• Binding: Paperback

• Format: Import

• Release Date: 03-11-2022

• ISBN: 9783030888589

• Language: English

• Pages: 389

• Cover: Paperback

• Dimensions: 9.3 x 6.1 x 1.1 inches

About The Book:

Nonlinear Partial Differential Equations with Nonstandard Growth Conditions by Iwona Chlebicka offers an in-depth study of nonlinear partial differential equations (PDEs) that satisfy specific nonstandard growth conditions, extending polynomial, inhomogeneous, and fully anisotropic growth. The book delves into the unique property of these equations, where the growth conditions of the highest order operators lead to the formulation of equations in Musielak–Orlicz spaces. This extended framework introduces new proof concepts and generalizes formalism, calling for a broader functional analytic approach.

The first part of the book establishes the theoretical framework necessary for understanding these complex equations, making it an essential introduction to the topic. The second part applies this theoretical foundation to various types of PDEs, including abstract and parabolic equations, as well as PDEs from fluid and solid mechanics. For advanced readers, the book also includes a brief chapter on the homogenization of elliptic PDEs.

This book is a vital resource for researchers in the fields of PDEs and functional analysis, providing a comprehensive and rigorous exploration of this advanced area of mathematics.