# A Radial Derivative with Boundary Values of the Spherical Poisson Integral

Research paper by O. Dzagnidze

Indexed on: 01 Jan '99Published on: 01 Jan '99Published in: Georgian Mathematical Journal

#### Abstract

A formula of a radial derivative $$\frac{\partial }{{\partial r}}u_f (r,\theta ,\phi )$$ is obtained with the aid of derivatives with respect to θ and to Φ of the functions closely connected with the spherical Poisson integral $$u_f (r,\theta ,\phi )$$ and the boundary values are determined for $$\frac{\partial }{{\partial r}}u_f (r,\theta ,\phi )$$. The boundary values are also found for partial derivatives with respect to the Cartesian coordinates $$\frac{\partial }{{\partial x}}u_F , \frac{\partial }{{\partial y}}u_F and \frac{\partial }{{\partial z}}u_F$$.