scholarly journals Second-order shape derivatives along normal trajectories, governed by Hamilton-Jacobi equations

2016 ◽  
Vol 54 (5) ◽  
pp. 1245-1266 ◽  
Author(s):  
G. Allaire ◽  
E. Cancès ◽  
J.-L. Vié
Keyword(s):  
Second Order ◽  
Shape Derivatives ◽  
Jacobi Equations

scholarly journals A Variational Method for Second Order Shape Derivatives

2016 ◽  
Vol 54 (2) ◽  
pp. 1056-1084 ◽  
Author(s):  
Guy Bouchitté ◽  
Ilaria Fragalà ◽  
Ilaria Lucardesi
Keyword(s):  
Variational Method ◽  
Second Order ◽  
Shape Derivatives

scholarly journals Multiscale problems and homogenization for second-order Hamilton–Jacobi equations

2007 ◽  
Vol 243 (2) ◽  
pp. 349-387 ◽  
Author(s):  
Olivier Alvarez ◽  
Martino Bardi ◽  
Claudio Marchi
Keyword(s):  
Second Order ◽  
Multiscale Problems ◽  
Jacobi Equations

scholarly journals Estimates of first and second order shape derivatives in nonsmooth multidimensional domains and applications

2016 ◽  
Vol 270 (7) ◽  
pp. 2616-2652 ◽  
Author(s):  
Jimmy Lamboley ◽  
Arian Novruzi ◽  
Michel Pierre
Keyword(s):  
Second Order ◽  
Shape Derivatives

scholarly journals The subdifferential of the sum of two functions in Banach spaces II. Second order case

1995 ◽  
Vol 51 (2) ◽  
pp. 235-248 ◽  
Author(s):  
Robert Deville ◽  
El Mahjoub El Haddad
Keyword(s):  
Hilbert Spaces ◽  
Type Theorem ◽  
Continuous Functions ◽  
Second Order ◽  
Infinite Dimensional ◽  
Jacobi Operators ◽  
Uniqueness Results ◽  
Lower Semi ◽  
Order Case ◽  
Jacobi Equations

We prove a formula for the second order subdifferential of the sum of two lower semi continuous functions in finite dimensions. This formula yields an Alexandrov type theorem for continuous functions. We derive from this uniqueness results of viscosity solutions of second order Hamilton-Jacobi equations and singlevaluedness of the associated Hamilton-Jacobi operators. We also provide conterexamples in infinite dimensional Hilbert spaces.

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