Duality theorems in some overdetermined boundary value problems

✍ Scribed by L. E. Payne; Philip W. Schaefer

• Publisher: John Wiley and Sons
• Year: 1989
• Tongue: English
• Weight: 558 KB
• Volume: 11
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670110606

✦ Synopsis

We consider several elliptic boundary value problems for which there is an overspecification ofdata on the boundary of the domain. After reformulating the problems in an equivalent integral form, we use the alternate integral formulation to deduce that if a solution exists. then the domain must be an N-ball. Various Green's functions and classical boundary value problems of second, fourth and higher order are included among the problems considered here.

Weinberger [1 1 J and was extended to a fourth-order problem by Bennett [2] and to certain semilinear systems of elliptic equations by Troy [lo]. Payne [8] addressed a similar question for equations with applications to elasticity while Garofalo and Lewis [4] extended Weinberger's method of proof to partial differential equations other than Poisson's equation.