Olofsson, Anders A representation formula for radially weighted biharmonic functions in the unit disc. (English) Zbl 1086.31003 Publ. Mat., Barc. 49, No. 2, 393-415 (2005). 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. Reviewer: Dagmar Medková (Praha) Cited in 1 ReviewCited in 6 Documents MSC: 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions 35J40 Boundary value problems for higher-order elliptic equations Keywords:radially weighted biharmonic operator; harmonic compensator PDFBibTeX XMLCite \textit{A. Olofsson}, Publ. Mat., Barc. 49, No. 2, 393--415 (2005; Zbl 1086.31003) Full Text: DOI EuDML