LOCAL SOLVABILITY OF A CONSTRAINED GRADIENT SYSTEM OF TOTAL VARIATIONPreprint Series # 609 This is the latest version of this item.
AbstractA 1harmonic map flow equation, a gradient system of total variation where values of unknowns are constrained in a compact manifold in R^N is formulated by use of subdifferentials of a singular energy  the total variation. An abstract convergence result is established to show that solutions of approximate problem converge to a solution of the limit problem. As an application of our convergence result a localintime solution of 1harmonic map flow equation is constructed as a limit of the solutions of pharmonic (p > 1) map flow equation, when the initial data is smooth with small total variation under periodic boundary condition.
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