## partial differential equation methods in control and shape analysis: lecture notes in pure and applied mathematics"Based on the International Federatiojn for Information Processing WG 7.2 Conference, held recently in Pisa, Italy. Provides recent results as well as entirely new material on control theory and shape analysis. Written by leading authorities from various desciplines." |

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### Contents

III | 1 |

IV | 11 |

V | 29 |

VI | 41 |

VII | 53 |

VIII | 63 |

IX | 77 |

X | 95 |

XV | 189 |

XVI | 205 |

XVII | 215 |

XVIII | 245 |

XIX | 259 |

XX | 275 |

XXI | 285 |

XXII | 293 |

### Common terms and phrases

Analysis Applications approximation assume Banach spaces boundary condition boundary control boundary value problem bounded characteristic function characterixation compact compute consider constant continuous convergence convex crack defined definition denote differentiahle Dirichlet Dirichlet problem domain dynamic programming energy functional estimate exists finite element formulation geometry given Hilbert space inequality integral J.P. ZOLESIO Jd Jd Jn\s Lemma linear Lipschitx mapping material derivative Math method minimixation minimizing minimum Moreover nonlinear obtain open set operator optimal control optimal control problem optimality conditions optimixation problem parameter Partial Differential Equations perturhation Proposition prove recall Remark respect result Riccati equations right hand side saddle point satisfies semiconcave semigroup sequence shape boundary derivative shape derivative shape optimixation smooth Soholev space Sophia Antipolis subset Theory unique solution Universita variable variational vector field viscosity solutions weakly zero