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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 \(\frac{\partial }{{\partial x}}u_F , \frac{\partial }{{\partial y}}u_F and \frac{\partial }{{\partial z}}u_F \).