TY - JOUR
T1 - Fully non-linear degenerate elliptic equations in complex geometry
AU - Chu, Jianchun
AU - McCleerey, Nicholas
N1 - Funding Information:
Acknowledgments: The authors were partially supported by NSF RTG grant DMS-1502632 . We would also like to thank Valentino Tosatti for helpful discussions.
Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/11/1
Y1 - 2021/11/1
N2 - We derive an a priori real Hessian estimate for solutions of a large family of geometric fully non-linear elliptic equations on compact Hermitian manifolds, which is independent of a lower bound for the right-hand side function. This improves on the estimates of Székelyhidi [57] and additionally applies to elliptic equations with a degenerate right-hand side. As an application, we establish the optimal C1,1 regularity of envelopes of (θ,m)-subharmonic functions on compact Hermitian manifolds.
AB - We derive an a priori real Hessian estimate for solutions of a large family of geometric fully non-linear elliptic equations on compact Hermitian manifolds, which is independent of a lower bound for the right-hand side function. This improves on the estimates of Székelyhidi [57] and additionally applies to elliptic equations with a degenerate right-hand side. As an application, we establish the optimal C1,1 regularity of envelopes of (θ,m)-subharmonic functions on compact Hermitian manifolds.
KW - Compact Hermitian manifolds
KW - Fully non-linear degenerate elliptic equations
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U2 - 10.1016/j.jfa.2021.109176
DO - 10.1016/j.jfa.2021.109176
M3 - Article
AN - SCOPUS:85110203588
SN - 0022-1236
VL - 281
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 9
M1 - 109176
ER -