A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces

By Iwona Chlebicka. Nonlinear Analysis, 2018

138 citations recorded by the source corpus.

Abstract The Musielak–Orlicz setting unifies 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dd6cb0d6ad501d97e53adc8bf190e865aef7c606

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

A variational approach to parabolic equations under general and p,q-growth conditions (2020, background): “Among them there are variational integrands fulfilling a standard growth condition from below and above, functionals of non-standard p, q−growth and double phase (as in [4–6,23,24] and [21,29,34,35]), functionals with exponential growth (see [7,44,46]), variable exponents [21,26,33,36,37] and Orlicz”
Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021, background): “For an overview of results we mention and the recent survey [54].”
Growth conditions and regularity for weak solutions to nonlinear elliptic pdes (2020, methodology): “For related recent references we also quote Duzgun-Marcellini-Vespri [39], [40], Rǎdulescu-Zhang [63], [64], Cencelja-Rădulescu-Repovš [19], Papageorgiou-Rădulescu-Repovš-Dušan [62], Ambrosio-Rădulescu [1], Ragusa-Tachikawa [65], Chlebicka [20], Chlebicka-DeFilippis [21], [22], CupiniGiannetti-Giov”