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Lppolyharmonic Dirichlet Problems in the Upper Half Plane

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Advances in Pure Mathematics 2015年第14期5卷 828-834页

作者： Kanda Pan Department of Mathematics Jinan University Guangzhou China

In this article, a class of Dirichlet problem with Lp boundary data for poly-harmonic function in the upper half plane is mainly investigated. By introducing a sequence of kernel functions called higher order Poisson kernels and a hierarchy of integral operators called higher order Pompeiu operators, we obtain a main result on integral representation solution as well as the uniqueness of the polyharmonic Dirichlet problem under a certain estimate.

关键词： Dirichlet Problem polyharmonic Function Higher Order Poisson Kernels Higher Order Pompeiu Operators Non-Tangential Maximal Function Uniqueness

Existence of Solutions to a Class of Navier Boundary Value Problem Involving the polyharmonic

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Advances in Pure Mathematics 2018年第4期8卷 373-379页

作者： Yongyi Lan School of Sciences Jimei University Xiamen China

This paper is devoted to the following high order elliptic problems under the Navier boundary condition: ?Without assuming the standard subcritical polynomial growth condition ensuring the compactness of a bounded (P.S.) sequence, we show that the Navier boundary value problem has at least a weak nontrivial solution for all λ>0?by using mountain pass theorem.

关键词： Navier Boundary Value Problem polyharmonic Variational Methods Mountain Pass Theorem

Mean-Value Theorems for Harmonic Functions on the Cube in Rn

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Advances in Pure Mathematics 2015年第11期5卷 683-688页

作者： Petar Petrov Faculty of Mathematics and Informatics Sofia University Sofia Bulgaria

Let be a hypercube in Rn. We prove theorems concerning mean-values of harmonic and polyharmonic functions on In(r), which can be considered as natural analogues of the famous Gauss surface and volume mean-value formulas for harmonic functions on the ball in and their extensions for polyharmonic functions. We also discuss an application of these formulas—the problem of best canonical one-sided L1-approximation by harmonic functions on In(r).

关键词： Harmonic Functions polyharmonic Functions Hypercube Quadrature Domain Best One-Sided Approximation

Effective Solution of Riemann Problem for Fifth Order Improperly Elliptic Equation on a Rectangle

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American Journal of Computational Mathematics 2012年第4期2卷 282-286页

作者： Seyed Mohammadali Ali. Raeisian Institute of Mathematics Armenian National Academy of Sciences Yerevan Armenia

In this paper we present a numerical method for solving Riemann type problem for the fifth order improperly elliptic equation in complex plane .We reduce this problem to the boundary value problems for properly ellipt... 详细信息

关键词： polyharmonic Equation Boundary Value Problem Dirichlet Problem Improperly Elliptic Equation Riemann Problem Grid Method