An imbedding theorem for Musielak–Sobolev spaces

By Xianling Fan. 2012

81 citations recorded by the source corpus.

Abstract Let Ω be a bounded domain in R N and A ∈ C 1 − 0 ( Ω ¯ × [ 0 , + ∞ ) ) be a Musielak–Orlicz function. We established an imbedding theorem for the Musielak–Sobolev space W 1 , A ( Ω ) of the form W 1 , A ( Ω ) ↪ L A ∗ ( Ω ) , where A ∗ is the Sobolev conjugate function of A , a Musielak–Orlicz function defined in the paper. This theorem extends the imbedding theorem established by Donaldson and Trudinger for Orlicz–Sobolev spaces to the case of Musielak–Sobolev spaces.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/30581f0e2a45d551ee60b09cc618560220717e8d

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, background): “2) is based on general embedding results of Musielak-Orlicz Sobolev spaces obtained by Fan [29] under the additional condition q p− < 1 + 1 N with q and p being the maximum and minimum of q and p on Ω, respectively.”
Nonlinear parabolic problems in Musielak--Orlicz spaces (2013, methodology): “In [15] the case of only x dependent modulars was considered and since this is not the main concern of the current paper we shall not extend it for the (t, x)−dependent case.”
An existence result for singular Finsler double phase problems (2020, background): “So far, it is not clear what is the optimal critical exponent for Musielak-Orlicz Sobolev spaces even when F is the Euclidean norm, see, for example, the paper of Fan [18].”
Hölder regularity of quasiminimizers under generalized growth conditions (2017, methodology): “However, this belief has been challenged recently, based on new techniques that were developed and perfected in the context of variable exponent spaces [11, 13, 19, 20, 24, 27, 28, 29, 30, 35, 36, 42].”