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Strong Convergence of Numerical Solutions to Degenerate Variational Problems

Roy A. Nicolaides

出版	Carnegie Mellon University, Department of Mathematics [Center for Nonlinear Analysis], 1992
URL	http://books.google.com.hk/books?id=8j8ItwAACAAJ&hl=&source=gbs_api

註釋

Abstract: "Numerical approximations of strongly degenerate variational problems of the form J(u) = F 01 F(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[superscript 1,p]. Rates in weaker norms and the connection with non-convex variational problems are also considered."