Stable Approximations of a Minimal Surface Problem with Variational Inequalities

M. Zuhair Nashed and Otmar Scherzer

Abstract and Applied Analysis, 1997, vol. 2, issue 1-2, 137-161

Abstract: 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) + ∫∂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 i(∂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.

Date: 1997
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https://doi.org/10.1155/S1085337597000316

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2:y:1997:i:1-2:p:137-161

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