\(L^p\) polyharmonic Dirichlet problems in regular domains. II: The upper half plane

DOI10.1016/j.jde.2011.08.024zbMath1256.31002OpenAlexW1981434541MaRDI QIDQ652504

Tao Qian, Zhihua Du, Jinxun Wang

Publication date: 14 December 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2011.08.024

zbMATH Keywords

polyharmonic functionsRiquier problem\(L^p\) datapolyharmonic Poisson kernelshalf planeNavier problem

Mathematics Subject Classification ID

Integral representations, integral operators, integral equations methods in two dimensions (31A10) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30) Higher-order elliptic equations (35J30) Other generalizations of analytic functions (including abstract-valued functions) (30G30)

Related Items

Riemann boundary-value problem for doubly-periodic bianalytic functions, Integral Representations Related to Complex Partial Differential Operators, Higher order Poisson kernels and \(L^p\) polyharmonic boundary value problems in Lipschitz domains, \(L^p\) polyharmonic Dirichlet problems in regular domains. IV: The upper-half space, L^p polyharmonic Robin problems on Lipschitz domains, L^ppolyharmonic Dirichlet problems in regular domains III: The unit ball, A note on Riemann problems for single-periodic polyanalytic functions, Riemann–Hilbert problems with Carleman shift and conjugation for polynomial Beltrami equations, On Riemann problem of automorphic polyanalytic functions connected with a rotation group, Riemann-Hilbert problems with shift on the Lyapunov curve for null-solutions of iterated Beltrami equations

Cites Work

• The Schwarz problem for polyanalytic functions
• The \(L^p\) Dirichlet problem for elliptic systems on Lipschitz domains
• A Dirichlet problem for polyharmonic functions
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation
• Decompositions of functions and Dirichlet problems in the unit disc
• The biharmonic Neumann problem in Lipschitz domains
• On Boundary Value Problems of Polyanalytic Functions on the Real Axis
• Partial Differential Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item