Some comparison results and a partial bang-bang property for two-phases problems in balls

Idriss Mazari (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper, we present two type of contributions to the study of two-phases problems. In such problems, the main focus is on optimising a diffusion function a under L ∞ and L 1 constraints, this function a appearing in a diffusive term of the form −∇ • (a∇) in the model, in order to maximise a certain criterion. We provide a parabolic Talenti inequality and a partial bang-bang property in radial geometries for a general class of elliptic optimisation problems: namely, if a radial solution exists, then it must saturate, at almost every point, the L ∞ constraints defining the admissible class. This is done using an oscillatory method.

Mots clés: Optimisation; Optimal Control of PDEs; Two-Phases Problems; Talenti Inequality

Domaines: Mathématiques [math]

Idriss Mazari. Some comparison results and a partial bang-bang property for two-phases problems in balls. Mathematics in Engineering, 2022. ⟨hal-03510093⟩