OnLp(x)norms

Edmunds, D. E.; Lang, Ján; Nekvinda, Aleš

doi:10.1098/rspa.1999.0309

Cited by 144 publications

(38 citation statements)

References 2 publications

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“…For more details we refer to the book by Musielak [20] and the papers by Acerbi at al., Edmunds et al [6,7,8], Kovacik and Rákosník [15], Mihȃilescu and Rȃdulescu [16], Samko and Vakulov [22], Zhikov [24].…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

“…By Example 2 on p. 243 in [5] we know that p 0 = p and p 0 = p + r and thus relation (6) in Theorem 1 is satisfied. On the other hand, by Proposition 1 in [18] (see also [17]) we deduce that relations (2) and (7) are fulfilled.…”

Section: Examplesmentioning

confidence: 99%

“…We point out that by relation (6) and the definition of p 0 we have q − < l ≤ p 0 . By the above inequality we remark that if we define…”

Section: Proof Of Theoremmentioning

confidence: 99%

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A continuous spectrum for nonhomogeneous differential operators in Orlicz-Sobolev spaces

Mihăilescu¹,

Rădulescu²

2009

MATH. SCAND.

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Abstract. We study the nonlinear eigenvalue problem −div(a(|∇u|)∇u) = λ|u| q(x)−2 u in Ω, u = 0 on ∂Ω, where Ω is a bounded open set in R N with smooth boundary, q is a continuous function, and a is a nonhomogeneous potential. We establish sufficient conditions on a and q such that the above nonhomogeneous quasilinear problem has continuous families of eigenvalues. The proofs rely on elementary variational arguments. The abstract results of this paper are illustrated by the cases a(t) = t p−2 log(1 + t r ) and a(t) = t p−2 [log(1 + t)] −1 .

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Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

Section: Examplesmentioning

confidence: 99%

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A continuous spectrum for nonhomogeneous differential operators in Orlicz-Sobolev spaces

Mihăilescu¹,

Rădulescu²

2009

MATH. SCAND.

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“…We refer the reader to the book of J. Musielak [20] and the papers of O. Kovacik and J. Rákosník [14], H. G. Leopold [15], D. Edmunds et al [6], [7], [8] and X. L. Fan et al [9], [12].…”

Section: P(x)mentioning

confidence: 99%

On a class of nonlinear problems involving a p(x)-Laplace type operator

Mihăilescu

2008

Czech Math J

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“…We also define variable exponent Lebesgue spaces (special cases of Orlicz spaces, see for example [6]) by…”

Section: Definition Of α(X)-multistable Measure and Integralmentioning

confidence: 99%

Multistable Processes and Localizability

Falconer

Liu

2012

Stochastic Models

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We use characteristic functions to construct α-multistable measures and integrals, where the measures behave locally like stable measures, but with the stability index α(x) varying with x. This enables us to construct α-multistable processes on R, that is processes whose scaling limit at time t is an α(t)-stable process. We present several examples of such multistable processes and examine their localisability.

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OnL^p(x)norms

Abstract: The relation between a Banach function space X and its subspaces formed by: (i) those functions with absolutely continuous norm; (ii) those with continuous norm; and (iii) the closure of the set of bounded functions are investigated in the case X = L p (x) .

Cited by 144 publications

References 2 publications

A continuous spectrum for nonhomogeneous differential operators in Orlicz-Sobolev spaces

A continuous spectrum for nonhomogeneous differential operators in Orlicz-Sobolev spaces

On a class of nonlinear problems involving a p(x)-Laplace type operator

Multistable Processes and Localizability

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