Asymptotic flatness of Morrey extremals

Hynd, Ryan; Seuffert, Francis

doi:10.1007/s00526-020-01827-0

Cited by 7 publications

(5 citation statements)

References 12 publications

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“…In particular, as supp(µ) is compact, u is p-harmonic on an exterior domain and is uniformly bounded. We can then conclude the following limits by our recent work [15]. Remark 4.5.…”

Section: Note That This Impliesmentioning

confidence: 58%

Extremals in nonlinear potential theory

Hynd¹,

Seuffert²

2020

Preprint

Self Cite

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“…In particular, as supp(µ) is compact, u is p-harmonic on an exterior domain and is uniformly bounded. We can then conclude the following limits by our recent work [15]. Remark 4.5.…”

Section: Note That This Impliesmentioning

confidence: 58%

Extremals in nonlinear potential theory

Hynd¹,

Seuffert²

2020

Preprint

Self Cite

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“…As a result, {u ≥ c} is a convex subset of the x n > 0 half space for each c ∈ (0, 1]. Furthermore, we established the limit lim |x|→∞ u(x) = 0 [20]. Consequently, {u ≥ c} is also compact for each c ∈ (0, 1].…”

Section: Monotonicity From the Axis Of Symmetrymentioning

confidence: 81%

On the symmetry and monotonicity of Morrey extremals

Hynd¹,

Seuffert²

2019

Preprint

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We employ Clarkson's inequality to deduce that each extremal of Morrey's inequality is axially symmetric and is antisymmetric with respect to reflection about a plane orthogonal to its axis of symmetry. We also show that each extremal is monotone in the distance from its axis of symmetry and monotone in the direction of its axis when restricted to spheres centered at the intersection of its axis and its antisymmetry plane.

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“…(b) S 2 −k (v j )≤2 kβ , for all k such that 2 −k r j ≥1, (c) Δ p v j =0 in R n \B 1 r j . Using local estimates for the p-Laplace equation, we may therefore extract a subsequence converging locally uniformly in R n \{0} to a function v. We also note that by Corollary 4.2 in [7], we know that…”

mentioning

confidence: 93%

Decay of extremals of Morrey’s inequality

Hynd,

Larson,

Lindgren

2024

Arkiv För Matematik

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We study the decay (at infinity) of extremals of Morrey's inequality in R n . These are functions satisfying supwhere p>n and C(p, n) is the optimal constant in Morrey's inequality. We prove that if n≥2 then any extremal has a power decay of order β for any, for all functions whose first order partial derivatives belong to L p (R n ). In a series of papers (cf.[7]-[9]), Hynd and Seuffert study this inequality and prove that there is a smallest constant C >0 such that (1.1) holds and that there are extremals of this inequality. An extremal is a function for which equality is attained in (1.1). They also prove that up to translation, rotation, dilatation and multiplication by a constant, any extremal function u satisfies 1. −Δ p u=c(δ en −δ −en ) in R n for a constant c>0,

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Asymptotic flatness of Morrey extremals

Cited by 7 publications

References 12 publications

Extremals in nonlinear potential theory

Extremals in nonlinear potential theory

On the symmetry and monotonicity of Morrey extremals

Decay of extremals of Morrey’s inequality

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