| Abstract: |
| Motivated by applications in image processing, we study asymptotic behavior for power curvature flow as the exponent tends to infinity. More precisely, we consider the level set formulation of the power curvature flow with a Lipschitz initial value. It is well known that for any given exponent there exists a unique viscosity solution. In this talk, we are interested in the limit behavior of such a solution as the exponent tends to infinity, which has applications in image denoising.
When the initial value satisfies a convexity assumption, we show that the limit equation can be characterized as the following stationary obstacle problem involving 1-Laplacian. The large exponent behavior is more complicated when the convexity assumption of the initial value is dropped. In this case, we will mainly discuss a simplified problem with another application related to a math model describing unstable sandpiles.
Part of this talk is based on joint work with Naoki Yamada at Fukuoka University. |
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