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Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces (Hardcover, 1st ed. 2021)
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Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces (Hardcover, 1st ed. 2021)
Series: Springer Monographs in Mathematics
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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.
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