A representation formula for radially weighted biharmonic functions in the unit disc (Q2574023)

The paper deals with the weighted biharmonic Dirichlet problem \(\Delta w^{-1}\Delta u=0\) in \(D\), \(u=f_0\) on \(\partial D\), \(\partial_n u=f_1\) on \(\partial D\). Here \(D\) is the unit disc in the plane, \(w\) is a radial continuous weight function and the boundary data \(f_0\), \(f_1\) are distributions on \(\partial D\). Unique solvability of the problem is proved under assumptions that \(\int w(t)\,dt<\infty \) and \(\int t^{2| k| +1}w(t)\,dt \geq c(1+| k| )^{-N}\) for \(k\in Z\). The solution of the problem is constructed.