Some Generalized Problems for Polyharmonic Functions

✍ Scribed by Janina Wolska-Bochenek; Marian Majchrowski

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 504 KB
• Volume: 19
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(19960725)19:11<883::aid-mma800>3.0.co;2-f

✦ Synopsis

In the first section of this paper, some non-local boundary value problem for the polyharmonic equation in the plane is considered. This problem consists in determining solution of the polyharmonic equation satisfying some special non-local-type boundary condition on two curves. The existence theorem is proved. In the second section, an example for the case of the biharmonic equation is considered. In the third section, some non-local, non-linear problem of Riquier type is examined. The Riquier-type problem consists in determining the polyharmonic function in the plane whose value together with its successive Laplacians are prescribed on the boundary. The existence theorem is proved and an example for the case of the biharmonic equation is considered.