TY - JOUR
T1 - Optimal rearrangement problem and normalized obstacle problem in the fractional setting
AU - Bonder, Julián Fernández
AU - Cheng, Zhiwei
AU - Mikayelyan, Hayk
N1 - Publisher Copyright:
© 2020 J.F. Bonder et al., published by De Gruyter 2020.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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.
AB - 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.
KW - Fractional partial differential equations
KW - Obstacle problem
KW - Optimization problems
UR - http://www.scopus.com/inward/record.url?scp=85085874293&partnerID=8YFLogxK
U2 - 10.1515/anona-2020-0067
DO - 10.1515/anona-2020-0067
M3 - Article
AN - SCOPUS:85085874293
SN - 2191-9496
VL - 9
SP - 1592
EP - 1606
JO - Advances in Nonlinear Analysis
JF - Advances in Nonlinear Analysis
IS - 1
ER -