Existence and Regularity For The Generalized Mean Curvature Flow Equations

Details Existence and Regularity For The Generalized Mean Curvature Flow Equations Existence and Regularity For The Generalized Mean Curvature Flow Equations

2009-08-21

arxiv.org/abs/0908.3057v1

Mathematics

Analysis of PDEs

13pages

Scientific paper

By making use of the approximation method, we obtain the existence and regularity of the viscosity solutions for the generalized mean curvature flow. The asymptotic behavior of the flow is also considered. In particular, the Dirichlet problem of the degenerate elliptic equation $$ -|\nabla v|(\mathrm{div}(\frac{\nabla v}{|\nabla v|})+\nu)=0 $$ is solvable in viscosity sense.

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