Bulanyi, Bohdan
[UCL]
Lemenant, Antoine
[IECL UMR 7502, Université de Lorraine, Nancy]
In this paper we prove a partial $C^{1,\alpha}$ regularity result in dimension $N=2$ for the optimal $p$-compliance problem, extending for $p\neq 2$ some of the results obtained by Chambolle et al. (2017). Because of the lack of good monotonicity estimates for the $p$-energy when $p\neq 2$, we employ an alternative technique based on a compactness argument leading to a $p$-energy decay at any flat point. We finally obtain that every optimal set has no loop, is Ahlfors regular, and is $C^{1,\alpha}$ at $\mathcal{H}^1$-a.e. point for every $p \in (1, +\infty)$.
Bibliographic reference |
Bulanyi, Bohdan ; Lemenant, Antoine. Regularity for the planar optimal $p$-compliance problem. In: ESAI M: Control, Optimisation and Calculus of Variations, Vol. 27, no. 35, p. 51 p. (2021) |
Permanent URL |
http://hdl.handle.net/2078.1/271832 |