On some properties of solutions of the biharmonic equation

DOI10.1016/j.amc.2005.11.013zbMath1098.31002OpenAlexW2086031894MaRDI QIDQ2496371

Yanyan Li

Publication date: 12 July 2006

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2005.11.013

zbMATH Keywords

harmonic functionsunivalent functionsbiharmonic functionsstarlike domainscomplex linear differential operator

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items (28)

Geometric properties of log-polyharmonic mappings ⋮ On Janowski type \(p\)-harmonic functions associated with generalized Sǎlǎgean operator ⋮ Construction and determination of univalent biharmonic mappings ⋮ On the univalence of polyharmonic mappings ⋮ Landau-type theorems for p-harmonic mappings or log-p-harmonic mappings ⋮ On certain geometric properties of polyharmonic mappings ⋮ Estimates on Bloch constants for certain \(\log\)-\(p\)-harmonic mappings ⋮ Estimate on the Bloch constant for certain harmonic mappings under a differential operator ⋮ Landau's theorem for log-\(p\)-harmonic mappings ⋮ Quasiconformal extensions of biharmonic mappings and strongly starlike biharmonic mappings ⋮ On lengths, areas and Lipschitz continuity of polyharmonic mappings ⋮ Landau's theorems for biharmonic mappings (II) ⋮ Landau-type theorems for certain biharmonic mappings ⋮ Univalent harmonic and biharmonic mappings with integer coefficients in complex quadratic fields ⋮ Representation formula and bi-Lipschitz continuity of solutions to inhomogeneous biharmonic Dirichlet problems in the unit disk ⋮ One parameter family of univalent biharmonic mappings ⋮ On the properties of a class of log-biharmonic functions ⋮ On certain classes of biharmonic mappings defined by convolution ⋮ Landau's theorem for polyharmonic mappings ⋮ Bloch constant and Landau's theorem for planar \(p\)-harmonic mappings ⋮ One parameter family of univalent polyharmonic mappings ⋮ Schwarzian derivative, integral means, and the affine and linear invariant families of biharmonic mappings ⋮ Compositions of polyharmonic mappings ⋮ Dirichlet problem, univalency and Schwarz lemma for biharmonic mappings ⋮ Landau's theorem for certain biharmonic mappings ⋮ Coefficient estimates and radii problems for certain classes of polyharmonic mappings ⋮ Properties of a class of \(p\)-harmonic functions ⋮ Landau-Bloch theorems for bounded biharmonic mappings

Cites Work

• Unnamed Item
• On the univalence of the log-biharmonic mappings.
• On univalent solutions of the biharmonic equation
• Harmonic Mappings onto Convex Domains
• Harmonic univalent functions
• Biorthogonal Series Solution of Stokes Flow Problems in Sectorial Regions
• On the Hankel determinants of univalent functions
• Slow Viscoelastic Flow at Large Distance From an Axis of Symmetry

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