Local solvability of a constrainedgradient system of total variation

Yoshikazu Giga, Yohei Kashima and Noriaki Yamazaki

Abstract and Applied Analysis, 2004, vol. 2004, issue 8, 651-682

Abstract: A 1‐harmonic map flow equation, a gradient system of total variation where values of unknowns are constrained in a compact manifold in ℝN, is formulated by the 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 local‐in‐time solution of 1‐harmonic map flow equation is constructed as a limit of the solutions of p‐harmonic (p > 1) map flow equation, when the initial data is smooth with small total variation under periodic boundary condition.

Date: 2004
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https://doi.org/10.1155/S1085337504311048

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2004:y:2004:i:8:p:651-682

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