- 期刊
STABLE APPROXIMATIONS OF A MINIMAL SURFACE PROBLEM WITH VARIATIONAL INEQUALITIES
並列摘要
In this paper we develop a new approach for the stable approximation of a minimal surface problem associated with a relaxed Dirichlet problem in the space BV(Ω) of functions of bounded variation. The problem can be reformulated as an unconstrained minimization problem of a functional J on BV(Ω) defined by J (u) = A(u) + S_(∂Ω) |Tu − φ|, where A(u) is the ＂area integral＂ of u with respect to Ω, T is the ＂trace operator＂ from BV(Ω) into L^1(∂Ω), and φ is the prescribed data on the boundary of Ω. We establish convergence and stability of approximate regularized solutions which are solutions of a family of variational inequalities. We also prove convergence of an iterative method based on Uzawa's algorithm for implementation of our regularization procedure.
並列關鍵字
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