Calderón-Zygmund estimates for generalized double phase problems

Baasandorj, Sumiya; Byun, Sun‐Sig; Oh, Jehan

doi:10.1016/j.jfa.2020.108670

Cited by 28 publications

(13 citation statements)

References 44 publications

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“…Then We refer to Sections 2.1 and 4 for more details on the terminology adopted in the above statement. A result analogous to the one described in Theorem 1 has been obtained in [4,Theorem 4.1] for generalized [3,19] triple phase problems, which in principle include also our functional H(•). However, in [4] to prove estimates similar to (1.3)- (1.4), extra technical assumptions on {α ν } κ ν=1 are required, i.e.…”

Section: Introductionsupporting

confidence: 58%

Optimal gradient estimates for multi-phase integrals

Filippis¹

2021

Preprint

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Section: Introductionsupporting

confidence: 58%

Optimal gradient estimates for multi-phase integrals

Filippis¹

2021

Preprint

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“…Traditionally ∇ 2 is formulated as ϕ * satisfying ∆ 2 condition, but here it is formulated without any mentions of the conjugate function. This definition has been used in the literature for example in [3]. Lemma 2.5.…”

Section: We Say Thatmentioning

confidence: 99%

Sharp growth conditions for boundedness of maximal function in generalized Orlicz spaces

Harjulehto

Karppinen

2022

Ann. Fenn. Math.

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We study sharp growth conditions for the boundedness of the Hardy-Littlewood maximal function in the generalized Orlicz spaces. We assume that the generalized Orlicz function \(\phi(x,t)\) satisfies the standard continuity properties (A0), (A1) and (A2). We show that if the Hardy-Littlewood maximal function is bounded from the generalized Orlicz space to itself then \(\phi(x,t)/t^p\) is almost increasing for large \(t\) for some \(p>1\). Moreover we show that the Hardy-Littlewood maximal function is bounded from the generalized Orlicz space \(L^\phi(\mathbb{R}^n)\) to itself if and only if \(\phi\) is weakly equivalent to a generalized Orlicz function \(\psi\) satisfying (A0), (A1) and (A2) for which \(\psi(x,t)/t^p\) is almost increasing for all \(t>0\) and some \(p>1\).

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“…for uniformly all t > 0, where note that all implied constants only depend only on s(Φ). Now we state some important properties of functions of N (Ω), see [6,7,22] for their proofs.…”

Section: Notationsmentioning

confidence: 99%

“…Multi-phase: Ψ(x, t) := t p + a(x)t q + b(x)t s for 1 < p q, s, see for instance [7,38]. 6. Orlicz double phase: Ψ(x, t) := G(t) + a(x)H a (t), see for instance [6,22].…”

Section: Introductionmentioning

confidence: 99%

Regularity for Orlicz phase problems

Baasandorj,

Byun

2021

Preprint

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We provide comprehensive regularity results and optimal conditions for a general class of functionals involving Orlicz multi-phase of the type υ → Ω F (x, υ, Dυ) dx, (0.1) exhibiting non-standard growth conditions and non-uniformly elliptic properties.The model functional under consideration is given by the Orlicz multi-phase integralwhere G, H k are N -functions and 0Its ellipticity ratio varies according to the geometry of the level sets {a k (x) = 0} of the modulating coefficient functions a k (•) for every k ∈ {1, . . . , N }.We give a unified treatment to show various regularity results for such multi-phase problems with the coefficient functions {a k (•)} N k=1 not necessarily Hölder continuous even for a lower level of the regularity. Moreover, assuming that minima of the functional in (0.2) belong to better spaces such as C 0,γ (Ω) or L κ (Ω) for some γ ∈ (0, 1) and κ ∈ (1, ∞], we address optimal conditions on nonlinearity for each variant under which we build comprehensive regularity results.On the other hand, since there is a lack of homogeneity properties in the nonlinearity, we consider an appropriate scaling with keeping the structures of the problems under which we apply Harmonic type approximation in the setting varying on the a priori assumption on minima. We believe that the methods and proofs developed in this paper are suitable to build regularity theorems for a larger class of non-autonomous functionals.

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Calderón-Zygmund estimates for generalized double phase problems

Cited by 28 publications

References 44 publications

Optimal gradient estimates for multi-phase integrals

Optimal gradient estimates for multi-phase integrals

Sharp growth conditions for boundedness of maximal function in generalized Orlicz spaces

Regularity for Orlicz phase problems

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