TY - GEN A1 - Sturm, Kevin T1 - Lagrange method in shape optimization for a class of non-linear partial differential equations: A material derivative free approach N2 - In this paper a new theorem is formulated which allows a rigorous proof of the shape differentiability without the usage of the 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. KW - Lagrange method, shape derivative, non-linear PDE, material derivative Y1 - 2014 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1297 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12977 ER -