Mean value properties for the Weinstein equation and modified dirac operators

We study the Weinstein equation u on the upper half space R3+. The Weinstein equation is connected to the axially symmetric potentials. We compute solutions of the Weinstein equation depending on the hyperbolic distance and x2. These results imply the explicit mean value properties. We also compute the fundamental solution. The main tools are the hyperbolic metric and its invariance properties.


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