On potential theory associated to a coupled PDE. (English) Zbl 1151.31010

Aliyev Azero─člu, Tahir (ed.) et al., Complex analysis and potential theory. Proceedings of the conference satellite to ICM 2006, Gebze, Turkey, September 8–14, 2006. Hackensack, NJ: World Scientific (ISBN 978-981-270-598-3/hbk). 178-186 (2007).
The author proposes some results concerning the Martin boundary and the restricted mean value property for harmonic functions associated to a harmonic structure given by coupled partial differential equations. In particular, the biharmonic equations \(\Delta^2\varphi=0\) and \(\Delta^2\varphi=\varphi\) are treated.
For the entire collection see [Zbl 1124.30001].


31C35 Martin boundary theory
35J55 Systems of elliptic equations, boundary value problems (MSC2000)