@article{Mazari2023, 
author = {Idriss Mazari},
title = {Some comparison results and a partial bang-bang property for two-phases problems in balls},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {1},
pages = {1-23},
keywords = {optimisation, optimal control of PDEs, two-phases problems, Talenti inequality},
url = {https://www.sciopen.com/article/10.3934/mine.2023010},
doi = {10.3934/mine.2023010},
abstract = {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  L1 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.}
}