Calculus of Variations and Partial Differential Equations

Abstract

Calculus of variatious and partial differential equations : topics on geometrical evolution problems and degree theory I edited by G. Buttazzo, A. Marino, M.K. V. Murthy. p.cm. Includes bibliographical references and index.

Analysis of Iterative Methods for Solving a Ginzburg-Landau Equation

“…According to [29] (11) is called Ginzburg-Landau equation if u is vector valued resp. complex (which is the case for the setting considered in this paper).…”

“…A real valued solution u of (10) can be used to approximate mean curvature motion (cf. [29]): for every ε there exists a unique bounded solution u ε . For ε 0 the limit u ε approaches a function u with values ±1 and the interface moves according to mean curvature motion.…”

“…For ε 0 the limit u ε approaches a function u with values ±1 and the interface moves according to mean curvature motion. A rich mathematical theory on the limiting behavior has been developed (see, e.g., [29] and references therein). Much less theoretical analysis is available, when u is complex or vector valued.…”

“…Using that the Dirichlet data of v (k) is f , the scalar products can be estimated by using (29) in the following way…”

Solving constraint ill-posed problems using Ginzburg–Landau regularization functionals

“…where F is a nonlinear continuous operator from L 1 (Ω) into a Hilbert space Y . Here we discuss (1.1) with two different constraints:…”