guest ::
| Home > Articles > Published articles > A representation formula for radially weighted biharmonic functions in the unit disc |
| Home > Articles > Published articles > A representation formula for radially weighted biharmonic functions in the unit disc |
| Date: | 2005 |
| Abstract: | Let w : D → (0, ∞) be a radial continuous weight function. We consider the weighted biharmonic equation ∆w −1 ∆u = 0 in D with Dirichlet boundary conditions u = f0 and ∂n u = f1 on T = ∂D. Under some extra conditions on the weight function w, we establish existence and uniqueness of a distributional solution u of this biharmonic Dirichlet problem. Furthermore, we give a representation formula for the solution u. The key to our analysis is a series representation of Almansi type. |
| Rights: | Tots els drets reservats.  |
| Language: | Anglès |
| Document: | Article ; recerca ; Versió publicada |
| Published in: | Publicacions matemàtiques, V. 49 n. 2 (2005) p. 393-415, ISSN 2014-4350 |
