Continuity results with respect to domain perturbation for the fractional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>p</mml:mi></mml:math>-Laplacian

Baroncini, Carla; Bonder, Julián Fernández; Spedaletti, Juan F.

doi:10.1016/j.aml.2017.06.005

Cited by 4 publications

(4 citation statements)

References 23 publications

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“…In view of [25, propositions 2.8 and 3.8], following the arguments in the proof of theorem 3.13 with the pertinent changes, it can be obtained the following extension for the continuity of solutions with respect to the domain in the fractional case (cf. [4]).…”

Section: Extension To Nonlocal Operatorsmentioning

confidence: 99%

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Continuity of solutions for the Δ_ϕ-Laplacian operator

Cantizano

Salort

Spedaletti

2020

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Section: Extension To Nonlocal Operatorsmentioning

confidence: 99%

“…This kind of stability results were extended to a more general frameworks involving nonlinear (and/or non-local) operators with p-Laplacian type structure. See [3,4,9,10].…”

Section: Introductionmentioning

confidence: 99%

Continuity of solutions for the Δ_ϕ-Laplacian operator

Cantizano

Salort

Spedaletti

2020

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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“…In view of [25, Proposition 2.8 and Proposition 3.8], following the arguments in the proof of Theorem 3.13 with the pertinent changes, it can be obtained the following extension for the continuity of solutions with respect to the domain in the fractional case (c.f. [3]).…”

Section: Continuity Of Solutionsmentioning

confidence: 99%

“…This kind of stability results were extended to a more general frameworks involving nonlinear (and/or non-local) operators with p−Laplacian type structure. See [2,3,7,8].…”

Section: Introductionmentioning

confidence: 99%

Continuity of solutions for the phi-Laplacian operator

Cantizano,

Salort,

Spedaletti

2020

Preprint

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Random dynamics of non-autonomous fractional stochastic p-Laplacian equations on $${\mathbb {R}}^N$$

Wang

2020

Banach J. Math. Anal.

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This article is concerned with the random dynamics of a wide class of nonautonomous, non-local, fractional, stochastic p-Laplacian equations driven by multiplicative white noise on the entire space ℝ N . We first establish the wellposedness of the equations when the time-dependent non-linear drift terms have polynomial growth of arbitrary orders p, q ≥ 2 . We then prove that the equation has a unique bi-spatial pullback random attractor that is measurable, compact in L 2 (ℝ N ) ∩ L p (ℝ N ) ∩ L q (ℝ N ) and attracts all random subsets of L 2 (ℝ N ) under the topology of L 2 (ℝ N ) ∩ L p (ℝ N ) ∩ L q (ℝ N ) . In addition, we establish the upper semicontinuity of these attractors in L 2 (ℝ N ) ∩ L p (ℝ N ) ∩ L q (ℝ N ) when the density of noise shrinks to zero. The idea of uniform tail estimates and the method of asymptotic a priori estimates are applied to prove the pullback asymptotic compactness of the solutions in L 2 (ℝ N ) ∩ L p (ℝ N ) ∩ L q (ℝ N ) to overcome the non-compactness of Sobolev embeddings on ℝ N as well as the almost sure nondifferentiability of the sample paths of the Wiener process.

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Continuity results with respect to domain perturbation for the fractional p-Laplacian

Abstract: Abstract. In this paper we give sufficient conditions on the approximating domains in order to obtain the continuity of solutions for the fractional p−laplacian. These conditions are given in terms of the fractional capacity of the approximating domains.

Cited by 4 publications

References 23 publications

Continuity of solutions for the Δ_ϕ-Laplacian operator

Continuity of solutions for the Δ_ϕ-Laplacian operator

Continuity of solutions for the phi-Laplacian operator

Random dynamics of non-autonomous fractional stochastic p-Laplacian equations on $${\mathbb {R}}^N$$

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Continuity results with respect to domain perturbation for the fractional p-Laplacian

Abstract: Abstract. In this paper we give sufficient conditions on the approximating domains in order to obtain the continuity of solutions for the fractional p−laplacian. These conditions are given in terms of the fractional capacity of the approximating domains.

Cited by 4 publications

References 23 publications

Continuity of solutions for the Δϕ-Laplacian operator

Continuity of solutions for the Δϕ-Laplacian operator

Continuity of solutions for the phi-Laplacian operator

Random dynamics of non-autonomous fractional stochastic p-Laplacian equations on $${\mathbb {R}}^N$$

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Product

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Continuity of solutions for the Δ_ϕ-Laplacian operator

Continuity of solutions for the Δ_ϕ-Laplacian operator