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A representation formula for radially weighted biharmonic functions in the unit disc
Olofsson, A.

Data: 2005
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 49 n. 2 (2005) p. 393-415, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_49205_08

23 p, 181.7 KB

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