Regularity results for generalized double phase functionals

Byun, Sun‐Sig; Oh, Jehan

doi:10.2140/apde.2020.13.1269

Cited by 67 publications

(28 citation statements)

References 33 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: 57%

Optimal gradient estimates for multi-phase integrals

Filippis¹

2021

Preprint

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Section: Introductionsupporting

confidence: 57%

Optimal gradient estimates for multi-phase integrals

Filippis¹

2021

Preprint

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“…Proof. The proof is elementary as done for [22,Lemma 4.6]. The only difference lies in that we have an additional one phase.…”

Section: Basic Regularity Resultsmentioning

confidence: 99%

“…Proof. Essentially, the proof for the first two parts is similar to the one of [22,Theorem 3.1]. Since our assumptions are weaker than the assumptions considered there, we provide the detailed proof in any case.…”

Section: Absence Of Lavrentiev Phenomenonmentioning

confidence: 89%

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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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“…Starting from [9,10], the regularity for weak solutions to (1.5) and minimizers of corresponding variational integral has been exhaustively studied, see [2,4,11,14,15,37] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Hölder regularity for weak solutions to nonlocal double phase problems

Byun¹,

Ok²,

Song³

2021

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We prove local boundedness and Hölder continuity for weak solutions to nonlocal double phase problems concerning the following fractional energy functionalwhere 0 < s ≤ t < 1 < p ≤ q < ∞ and a(•, •) ≥ 0. For such regularity results, we identify sharp assumptions on the modulating coefficient a(•, •) and the powers s, t, p, q which are analogous to those for local double phase problems.

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Regularity results for generalized double phase functionals

Cited by 67 publications

References 33 publications

Optimal gradient estimates for multi-phase integrals

Optimal gradient estimates for multi-phase integrals

Regularity for Orlicz phase problems

Hölder regularity for weak solutions to nonlocal double phase problems

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