The Inverse Problem for Asgeirsson's Mean Value Equality

关于Asgeirsson均值等式的反问题(英文)

For the linear partial differential operator with constant coefficients Lx = the sufficient and necessary conditions for all cm solutions u(x, y)of equation ( 4 ) satisfying Asgeirsson's mean value equality ( 2 ) are that Lx = c where a(≠ 0 ), c are constants, A, is the Laplacian.

对于常系数线性偏微分算子L_x=■a_aD_x^a,方程L_(x)u(x,y)=L_(y)u(x,y)的所有C^m解满足Asgcirsson均值等式的充分必要条件是L_x=c+a△_x,这里a(≠0),c为常数,△_x为Laplace算子.