CAJ | 학술논문

对n维多重非齐次调和方程△(k)u=f(x),x∈Rn,给出了基本解的递推公式以及多重调和函数的积分关系式.在非齐次项f(x)为m次调和的情形下将域上的积分转化为沿边界的积分,进而应用直接法给出了基本边界积分方程.对f(x)为一般光滑函数的情形,给出了用泰勒多项式逼近时相应的误差估计并证明了含误差项的积分是收敛的.
대n유다중비제차조화방정△(k)u=f(x),x∈Rn,급출료기본해적체추공식이급다중조화함수적적분관계식.재비제차항f(x)위m차조화적정형하장역상적적분전화위연변계적적분,진이응용직접법급출료기본변계적분방정.대f(x)위일반광활함수적정형,급출료용태륵다항식핍근시상응적오차고계병증명료함오차항적적분시수렴적.
In this paper, the n-dimensional multiple non-homogeneous harmonic equation △(k)u = f(x),x∈Rn, is considered. Firstly, the fundamental solution and its recurrence formulae are given. Then some fundamental integral relations are presented, specially, for multiple harmonic function. Under the assumption that non-homogeneous term f(x) is mdegree harmonic, the integral term in domain is shifted boundary integral, and hence the boundary integral equation without integral in domain is obtained. Finally, the error and convergence analysis is discussed by Taylor polynomial approximation of non-homogeneous term f(x).