Sobolev embeddings with variable exponent

By D. Edmunds, J. Rákosnik. 2000

595 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/86ff204d5114b5b1b1fa0ae5fa5692f5089ad07f

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

SOBOLEV AND JAWERTH EMBEDDINGS FOR SPACES WITH VARIABLE SMOOTHNESS AND INTEGRABILITY (2009, background): “Edmunds and Rákosńık [10, 11] proved the optimal Sobolev embedding theorem under Lipschitz and Hölder continuity of the exponents, cf.”
Entropy solutions for the p(x)-Laplace equation (2009, methodology): “Now, we give a useful result in order to apply the Sobolev inequality ( cf. [15]).”
On the existence of stationary solutions for higher-order p-Kirchhoff problems (2014, unknown): “1 of [20] and the continuity of the embedding [W L,p(·) 0 (Ω)] d ↪→ [LpL(·)(Ω)]d, we have for every u ∈ [W 0 (Ω)] |Ψ2(u)| ≤ ∫”
THE BOUNDEDNESS OF CLASSICAL OPERATORS ON VARIABLE L p SPACES (2006, background): “(See, for example, [1, 12, 15, 19, 30, 39, 46] and their references.”
Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space Lp(⋅)(logL)q(⋅) (2008, background): “In recent years, the generalized Lebesgue spaces have attracted more and more attention, in connection with the study of elasticity, fluid mechanics and differential equations with p(·)-growth; see for example Orlicz [29], Kováčik-Rákosńık [22], Edmunds-Rákosńık [7] and R ◦ užička [30].”
Sharp regularity for functionals with (p,q) growth (2004, background): “This space is currently the object of intensive investigations (see instance [17],[16]).”
An atomic decomposition of variable Besov and Triebel-Lizorkin spaces (2009, background): “Moreover, these spaces have been applied to partial differential equations and the calculus of variation, see [1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 16, 17, 18, 19, 21, 22, 29] and references therein.”