Some properties of a class of elliptic partial differential operators

Chen, Shaolin; Вуоринен, Матти

doi:10.1016/j.jmaa.2015.06.026

Cited by 31 publications

(5 citation statements)

References 26 publications

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“…Furthermore, by [20,22], we know that complex-valued kernel α−harmonic mappings are related to the real kernel α−harmonic mappings. For the related study on real kernel α−harmonic mappings, see [8,13,19].…”

Section: Introductions and Main Resultsmentioning

confidence: 99%

Some coefficient estimates on real kernel 𝛼-harmonic mappings

Long

Wang

2022

Proc. Amer. Math. Soc.

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We call the solution of a kind of second order homogeneous partial differential equation as real kernel α − \alpha - harmonic mappings. For this class of mappings, we explore its Heinz type inequality. Furthermore, for a subclass of real kernel α − \alpha - harmonic mappings with real coefficients, we estimate their coefficients. At last, we study the extremal function of Schwartz type lemma for the class of real kernel α − \alpha - harmonic mappings.

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Section: Introductions and Main Resultsmentioning

confidence: 99%

Some coefficient estimates on real kernel 𝛼-harmonic mappings

Long

Wang

2022

Proc. Amer. Math. Soc.

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“…To establish analogs of the Landau type theorem for more general classes of functions, it is necessary to restrict our focus on certain subclasses (cf. [1], [4], [5], [6], [7], [8], [9]).…”

Section: And Only If It Has a Series Expansion Of The Formmentioning

confidence: 99%

“…Theorem E. [9] For α > −1, let u ∈ C 2 (D) be a T α -harmonic function with the series expansion of the form (1.3) and sup z∈D |u(z)| ≤ M, where M > 0. Then, for k ∈ {1, 2, .…”

Section: And Only If It Has a Series Expansion Of The Formmentioning

confidence: 99%

Schwarz Lemma for mappings satisfying Biharmonic Equations

Khalfallah¹,

Haggui²,

Mhamdi³

2020

Preprint

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In this paper, we establish some Schwarz type lemmas for mappings Φ satisfying the inhomogeneous biharmonic Dirichlet problem ∆(∆(Φ)) = g in D, Φ = f on T and ∂ n Φ = h on T, where g is a continuous function on D, f, h are continuous functions on T, where D is the unit disc of the complex plane C and T = ∂D is the unit circle. To reach our aim, we start by investigating some properties of T 2 -harmonic functions. Finally, we prove a Landau-type theorem.

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“…Borichev and Hedenmalm [6] have established a connection to polyharmonic theory. Other recent related papers are [5,[8][9][10]14,16,17,22].…”

Section: Introductionmentioning

confidence: 99%