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Duality theorems in some overdetermined boundary value problems
Author(s) -
Payne L. E.,
Schaefer Philip W.
Publication year - 1989
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670110606
Subject(s) - mathematics , overdetermined system , boundary value problem , mathematical analysis , domain (mathematical analysis) , elliptic boundary value problem , ball (mathematics) , duality (order theory) , mixed boundary condition , order (exchange) , pure mathematics , finance , economics
We consider several elliptic boundary value problems for which there is an overspecification of data 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.