TY - GEN A1 - Druet, Pierre-Etienne T1 - Some mathematical problems related to the 2nd order optimal shape of a crystallization interface N2 - We consider the problem to optimize the stationary temperature distribution and the equilibrium shape of the solid-liquid interface in a two-phase system subject to a temperature gradient. The interface satisfies the minimization principle of the free energy, while the temperature is solving the heat equation with a radiation boundary conditions at the outer wall. Under the condition that the temperature gradient is uniformly negative in the direction of crystallization, the interface is expected to have a global graph representation. We reformulate this condition as a pointwise constraint on the gradient of the state, and we derive the first order optimality system for a class of objective functionals that account for the second surface derivatives, and for the surface temperature gradient. KW - Stefan-Gibbs-Thompson problem KW - Singularity of mean-curvature type KW - Optimal control KW - Pointwise gradient state constraints KW - First order optimality conditions Y1 - 2012 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1147 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-11470 ER -