A Partial Differential Equation for the Rank One Convex Envelope

  title={A Partial Differential Equation for the Rank One Convex Envelope},
  author={Adam M. Oberman and Yuanlong Ruan},
  journal={Archive for Rational Mechanics and Analysis},
  • Adam M. Oberman, Yuanlong Ruan
  • Published 2016
  • Mathematics
  • Archive for Rational Mechanics and Analysis
  • A partial differential equation (PDE) for the rank one convex envelope is introduced. The existence and uniqueness of viscosity solutions to the PDE is established. Elliptic finite difference schemes are constructed and convergence of finite difference solutions to the viscosity solution of the PDE is proven. Computational results are presented and laminates are computed from the envelopes. Results include the Kohn–Strang example, the classical four gradient example, and an example with eight… CONTINUE READING
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