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

DOI10.4171/IFB/366zbMath1353.49054OpenAlexW2530970253MaRDI QIDQ345901

Daniel Kraft

Publication date: 2 December 2016

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/ifb/366

zbMATH Keywords

level-set methodviscosity solutionsshape optimisationHopf-Lax formulashape sensitivity analysis

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Sensitivity analysis for optimization problems on manifolds (49Q12)

Related Items (1)

Measure-theoretic properties of level sets of distance functions

Cites Work

• Unnamed Item
• A framework for the construction of level set methods for shape optimization and reconstruction
• On the strong maximum principle for fully nonlinear degenerate elliptic equations
• A LEVEL SET BASED SHAPE OPTIMIZATION METHOD FOR AN ELLIPTIC OBSTACLE PROBLEM
• Convergence of a Generalized Fast-Marching Method for an Eikonal Equation with a Velocity-Changing Sign
• On Hopf's formulas for solutions of Hamilton-Jacobi equations
• Front Propagation and Phase Field Theory
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

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