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arXiv · 1804.04193

A pocket guide to nonlinear differential equations in the Musielak--Orlicz spaces

Iwona Chlebicka
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Abstract

The Musielak--Orlicz setting unifies the variable exponent, Orlicz, weighted Sobolev, and double-phase spaces. They inherit technical difficulties resulting from general growth and inhomogeneity. In this survey we present an overview of developments of the theory of existence of~PDEs in the setting including reflexive and non-reflexive cases, as well as isotropic and anisotropic ones. Particular attention is paid to problems with data below natural duality in absence of Lavrentiev's phenomenon.

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Iwona Chlebicka. 2018-05-04. A pocket guide to nonlinear differential equations in the Musielak--Orlicz spaces. https://doi.org/10.1016/j.na.2018.05.003

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