Optimal rearrangement problem and normalized obstacle problem in the fractional setting

2019/05/14 by Bonder, Julián Fernández, Cheng, Zhiwei, Mikayelyan, Hayk
#35J60 #35R11 #35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.05415

Abstract

We consider an optimal rearrangement minimization problem involving the fractional Laplace operator (-Δ)^s, 00\, which happens to be the fractional analogue of the normalized obstacle problem Δu=χ_\u>0\. A new section analyzing s → 1 has been added.

Related

• Fractional optimal maximization problem and the unstable fractional obstacle problem
• Constrained optimal rearrangement problem leading to a new type obstacle problem
• Optimization problems in rearrangement classes for fractional p-Laplacian equations
• Optimal regularity of solutions to the obstacle problem for the\n fractional Laplacian with drift
• Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian