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Taylor Series of Biharmonic Poisson Integral for Upper Half-Plane
The fourth-order partial differential equation for the biharmonic Poisson integral is presented in the case of the upper half-plane ( y > 0). To solve...
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On approximation of functions from Hölder classes by biharmonic Poisson integrals defined in the upper half-plane
The paper investigates the approximate properties of biharmonic Poisson integrals for the upper half-plane on the classes of Hölder functions in the...
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Quasiconformal Extensions of Biharmonic Map**s and Strongly Starlike Biharmonic Map**s
As a generalization of conformal map**s and planar harmonic map**s, biharmonic map**s have attracted more and more attention. This paper...
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Sharp well-posedness of the biharmonic Schrödinger equation in a quarter plane
We obtain an almost sharp local well–posedness result for the biharmonic equation on the quarter plane. In addition, we prove that the nonlinear part...
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Biharmonic Problem for an Angle and Monogenic Functions
We consider a piecewise continuous biharmonic problem in an angle and the corresponding Schwartz-type boundary-value problem for monogenic functions...
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Steklov–Neumann Biharmonic Problem in Weighted Spaces
AbstractWe consider the mixed biharmonic problem with the Steklov–Neumann boundary conditions with parameters in the exterior of a compact set under...
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A Novel Boundary Integral Formulation for the Biharmonic Wave Scattering Problem
This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the...
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Steklov–Farwig Biharmonic Problem in Exterior Domains
AbstractA biharmonic problem with the mixed Steklov–Farwig boundary conditions in the exterior of a compact set is considered under the assumption...
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On the solution of a complicated biharmonic equation in a hydroelasticity problem
A hydroelastic problem of free vibrations of a thin plate that horizontally separates ideal in-compressible liquids of different densities in a rigid...
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Mixed Biharmonic Problem with the Steklov-type and Neumann Boundary Conditions in Unbounded Domains
AbstractA biharmonic problem with mixed Steklov-type and Neumann conditions on the boundary in the exterior of a compact set is considered under the...
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Theorems of the Phragmén–Lindelöf Type for Biharmonic Functions
AbstractTheorems of the Phragmén–Lindelöf type for biharmonic functions, which is obtained using Carleman type formulas, is considered.
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Positive solutions for a class of biharmonic problems: existence, nonexistence and multiplicity
The main objective of this article is to consider a biharmonic problem with Navier boundary conditions. Among others, some criteria for the...
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On Schwarz–Pick-Type Inequality and Lipschitz Continuity for Solutions to Nonhomogeneous Biharmonic Equations
The purpose of this paper is to study the Schwarz–Pick type inequality and the Lipschitz continuity for the solutions to the nonhomogeneous...
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Invertibility Criteria for the Biharmonic Single-Layer Potential
While the single-layer operator for the Laplacian is well understood, questions remain concerning the single-layer operator for the Bilaplacian,...
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Error Estimates of Finite Difference Methods for the Biharmonic Nonlinear Schrödinger Equation
We present two finite difference time domain methods for the biharmonic nonlinear Schrödinger equation (BNLS) by reformulating it into a system of...
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Neumann Eigenvalues of the Biharmonic Operator on Domains: Geometric Bounds and Related Results
We study an eigenvalue problem for the biharmonic operator with Neumann boundary conditions on domains of Riemannian manifolds. We discuss the weak...
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The biharmonic Alt–Caffarelli problem in 2D
We examine a variational free boundary problem of Alt–Caffarelli type for the biharmonic operator with Navier boundary conditions in two dimensions....
