On a Property of Harmonic Functions

  • Ivan Keglević

    Fernuniversität-GHS Hagen, Germany


If we divide the space Rn\mathbb R^n into two disjoint areas with one common hypersurface and define a harmonic function in each part of these areas such that their gradients vanish at infinity and the normal components of their gradients are equal on the hypersurface, then for some hypersurfaces such as a circle in R2\mathbb R^2 or a hyperplane in Rn\mathbb R^n the sum of the tangential components of the gradients is zero. We investigate for which hypersurfaces we have this property and prove that such hypersurfaces in R2\mathbb R^2 are only circles and straight lines. We also give an application of this property to an ideal plane flow through a porous surface.

Cite this article

Ivan Keglević, On a Property of Harmonic Functions. Z. Anal. Anwend. 14 (1995), no. 1, pp. 15–24

DOI 10.4171/ZAA/659