A Hopf–Lax formula for the time evolution of the level-set equation and a new approach to shape sensitivity analysis

@inproceedings{Kraft2016AHF,
  title={A Hopf–Lax formula for the time evolution of the level-set equation and a new approach to shape sensitivity analysis},
  author={Daniel Kraft},
  year={2016}
}
The level-set method is used in many different applications to describe the propagation of shapes and domains. When scalar speed fields are used to encode the desired shape evolution, this leads to the classical level-set equation. We present a concise Hopf-Lax representation formula that can be used to characterise the evolved domains at arbitrary times. This result is also applicable for the case of speed fields without a fixed sign, even though the level-set equation has a non-convex… CONTINUE READING

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