Strong convergence of numerical solutions to degenerate variational problems

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."