INVESTIGADORES
FERNANDEZ BONDER Julian
artículos
Título:
Optimal rearrangement problem and normalized obstacle problem in the fractional setting
Autor/es:
BONDER, JULIÁN FERNÁNDEZ; CHENG, ZHIWEI; MIKAYELYAN, HAYK
Revista:
Advances in Nonlinear Analysis
Editorial:
De Gruyter
Referencias:
Año: 2020 vol. 9 p. 1592 - 1606
ISSN:
2191-9496
Resumen:
We consider an optimal rearrangement minimization problem involving the fractional Laplace operator (-Δ)s, 0 < s < 1, and the Gagliardo seminorm jujs. We prove the existence of the unique minimizer, analyze its properties as well as derive the non-local and highly non-linear PDE it satises -(-Δ)sU - x-(-Δ)sU+; 1 =U>0g, which happens to be the fractional analogue of the normalized obstacle problem Δu = xu>0.
