TY - JOUR
T1 - Interior W2,p estimate for small perturbations to the complex Monge–AmpÈre equation
AU - Cheng, Jingrui
AU - Xu, Yulun
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2023/11
Y1 - 2023/11
N2 - Let w be a bounded, C3 , strictly plurisubharmonic function defined on B1⊂ Cn . Then w has a neighborhood in L∞(B1) with the following property: for any continuous, plurisubharmonic function u in this neighborhood solving 1 - ε≤ MA(u) ≤ 1 + ε , one has u∈W2,p(B12) , as long as ε> 0 is small enough depending only on n and p. This partially generalizes Caffarelli’s interior W2,p estimates for real Monge–Ampère to the complex version.
AB - Let w be a bounded, C3 , strictly plurisubharmonic function defined on B1⊂ Cn . Then w has a neighborhood in L∞(B1) with the following property: for any continuous, plurisubharmonic function u in this neighborhood solving 1 - ε≤ MA(u) ≤ 1 + ε , one has u∈W2,p(B12) , as long as ε> 0 is small enough depending only on n and p. This partially generalizes Caffarelli’s interior W2,p estimates for real Monge–Ampère to the complex version.
UR - https://www.scopus.com/pages/publications/85172008105
U2 - 10.1007/s00526-023-02571-x
DO - 10.1007/s00526-023-02571-x
M3 - Article
AN - SCOPUS:85172008105
SN - 0944-2669
VL - 62
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 8
M1 - 231
ER -