WIAS Preprint No. 1817, (2013)

Lagrange method in shape optimization for non-linear partial differential equations: A material derivative free approach


  • Sturm, Kevin

2010 Mathematics Subject Classification

  • 49Q10 49Q12


  • Lagrange approach, shape derivative, non-linear partial differential equations, material derivative




This paper studies the relationship between the material derivative method, the shape derivative method, the min-max formulation of Correa and Seeger, and the Lagrange method introduced by Céa. A theorem is formulated which allows a rigorous proof of the shape differentiability without the usage of material derivative; the domain expression is automatically obtained and the boundary expression is easy to derive. Furthermore, the theorem is applied to a cost function which depends on a quasi-linear transmission problem. Using a Gagliardo penalization the existence of optimal shapes is established.

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