LOCAL SOLVABILITY OF A CONSTRAINED GRADIENT SYSTEM OF TOTAL VARIATION

By Yoshikazu Giga, Yohei Kashima, N. Yamazaki. 2003

52 citations recorded by the source corpus.

A 1-harmonic 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 subd-ifferentials 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e100f8613a62f95643d36cb3b60ad052e8db8689

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Mi-Ho Giga
2. Yoshikazu Giga

In Computational Theory and Mathematics

1. Yoshikazu Giga
2. Ken Abe

Citations in the corpus

• Very singular diffusion equations: second and fourth order problems (2010, background): “where u is a mapping to a unit sphere in R m . It is solvable locally-in-time [ 55 ].”