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Variational problems in Clifford analysis
Author(s) -
Dubinskii Julii,
Reissig Michael
Publication year - 2002
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.270
Subject(s) - mathematics , linear subspace , sobolev space , pure mathematics , scheme (mathematics) , galerkin method , dirichlet distribution , clifford analysis , dirichlet problem , mathematical analysis , boundary value problem , nonlinear system , dirac operator , physics , quantum mechanics
Using decomposition results for Sobolev spaces of Clifford‐valued functions into direct sums of subspaces of monogenic and co‐monogenic functions variational problems will be studied.These variational problems are equivalent to PD‐models by the choice of special operators of conboundary differentiation. By a Galerkin scheme we construct the monogenic part as a weak solution of a non‐linear problem. The co‐monogenic potential is the solution of a weak Dirichlet problem. Copyright © 2002 John Wiley & Sons, Ltd.