关于Asgeirsson均值等式的反问题(英文)

The Inverse Problem for Asgeirsson's Mean Value Equality

中文摘要:

      对于常系数线性偏微分算子(?),方程L_xu(x,y)=L_yu(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.

英文摘要:

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