partial differential equation methods in control and shape analysis: lecture notes in pure and applied mathematicsGiuseppe Da Prato, Jean-Paul Zolesio "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." |
Contents
III | 1 |
IV | 11 |
V | 29 |
VII | 41 |
VIII | 53 |
IX | 63 |
X | 77 |
XI | 95 |
XVI | 189 |
XVII | 205 |
XVIII | 215 |
XIX | 245 |
XX | 259 |
XXII | 275 |
XXIII | 285 |
XXIV | 293 |
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Analysis approximation assume Banach spaces boundary condition boundary control boundary value problem bounded compact compute consider constant continuous convergence convex defined definition DELFOUR denote Dirichlet Dirichlet problem domain Du.u estimate exists finite element geometry given H¹(N H¹(T Hilbert space inequality integral J.P. ZOLESIO L²(N Lemma linear Lipschitz continuity mapping material derivative Math minimizing Moreover nonlinear obtain operator optimal control optimal control problem optimality conditions parameter Partial Differential Equations perturbation Proof Proposition prove respect result Riccati equations right-hand side satisfies semiconcave semigroup sequence shape boundary derivative shape derivative shape optimization smooth Sobolev space Sophia Antipolis subset Theorem Theory unique solution Università variable variational vector field viscosity solutions weakly zero ZOLÉSIO дп მყ