Optimal rearrangement problem and normalized obstacle problem in the fractional setting

Abstract

We consider an optimal rearrangement minimization problem involving the fractional Laplace operator (–Δ)s, 0 < s < 1, and the Gagliardo seminorm |u|s. We prove the existence of the unique minimizer, analyze its properties as well as derive the non-local and highly non-linear PDE it satisfies

Keywords

• fractional partial differential equations
• optimization problems
• obstacle problem
• 35r11
• 35j60