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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Strong convergence of numerical solutions to degenerate variational problems


Authors: R. A. Nicolaides and Noel J. Walkington
Journal: Math. Comp. 64 (1995), 117-127
MSC: Primary 65N15; Secondary 65K10, 65N12
MathSciNet review: 1262281
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Abstract: Numerical approximations of strongly degenerate variational problems of the form $ J(u) = \smallint _0^1F(u' ) + {(u - f)^2}$ are considered, where F is assumed convex but may have intervals where $ F'' = 0$. It is shown that, in spite of the degeneracy, natural numerical approximations still converge in $ {W^{1,p}}$. Rates in weaker norms and the connection with nonconvex variational problems are also considered.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1995-1262281-0
PII: S 0025-5718(1995)1262281-0
Keywords: Approximation of degenerate variational problems
Article copyright: © Copyright 1995 American Mathematical Society