4 papers
Unstable free boundary problems in optimal control theory: existence and regularity
Lorenzo Ferreri, Idriss Mazari-Fouquer, Raphaël Prunier
We establish the first general regularity result for constrained optimal control problems arising naturally in mathematical physics and mathematical biology. Namely, we prove that…
Fuglede-type arguments for isoperimetric problems and applications to stability among convex shapes
Raphaël Prunier
This paper is concerned with stability of the ball for a class of isoperimetric problems under convexity constraint. Considering the problem of minimizing among c…
Sharp Quantitative Stability of the Dirichlet spectrum near the ball
Dorin Bucur, Jimmy Lamboley, Mickaël Nahon +1
Let be an open set with the same volume as the unit ball and let be the -th eigenvalue of the Laplace operator of with Dirichlet boundary…
Regularity in shape optimization under convexity constraint
Jimmy Lamboley, Raphaël Prunier
This paper is concerned with the regularity of shape optimizers of a class of isoperimetric problems under convexity constraint. We prove that minimizers of the sum of the perimete…