Overview of differential equations with non-standard growth

By Petteri Harjulehto, P. Hasto, Ut V. Le, Matti Nuortio. 2010

390 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4110bd77b245050a3838430b8fdb72eccda1b9b4

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Besov spaces with variable smoothness and integrability (2010, methodology): “For an overview we refer to the surveys [14, 21, 30, 36] and the monograph [13].”
On a p(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{p(x)}$$\end{document}-biharmonic problem with singula (2017, background): “Abstract setting To study p(x)-biharmonic problems, we need some results on the spaces L(Ω), W (Ω) and W (Ω); see [16,23,25,26] for details, complements and proofs.”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “Let us refer also to the survey [119] describing carefully developments of the theory of differential equations within the setting.”
Multiplicity of solutions for a class of anisotropic elliptic equations with variable exponent (2011, neutral): “For more details concerning the variable exponent spaces W 1,pð Þ 0 ð Þ we refer to the papers [9,38–41].”
Anisotropic nonlinear Neumann problems (2011, background): “A comprehensive survey of equations with nonstandard growth can be found in the recent paper of Harjulehto–Hästö-Lê–Nuortio [26], which has also a detailed bibliography.”
Extrapolation and interpolation in generalized Orlicz spaces (2018, background): “When φ(x, t) = t we get the variable Lebesgue spaces which have been extensively studied in the past 25 years [18, 24, 33], and when φ(x, t) = t + a(x)t, p < q, we get the double phase functional recently studied in [5, 13].”