Author:
Abja Soufian,Olive Guillaume
Abstract
AbstractIn this paper, we establish a local regularity result for $$W^{2,p}_{{\mathrm {loc}}}$$
W
loc
2
,
p
solutions to complex degenerate nonlinear elliptic equations $$F(D^2_{\mathbb {C}}u)=f$$
F
(
D
C
2
u
)
=
f
when they dominate the Monge–Ampère equation. Notably, we apply our result to the so-called k-Monge–Ampère equation.
Publisher
Springer Science and Business Media LLC
Reference28 articles.
1. Abja, S., Dinew, S., Olive, G.: Uniform estimates for concave homogeneous complex degenerate elliptic equations comparable to the Monge–Ampère equation, preprint: arXiv:2010.08434 (2020)
2. Błocki, Z., Dinew, S.: A local regularity of the complex Monge–Ampère equation. Math. Ann. 351(2), 411–416 (2011)
3. Błocki, Z.: On the regularity of the complex Monge–Ampère operator, Complex geometric analysis in Pohang (1997). Contemp. Math., vol. 222, pp. 181–189. Amer. Math. Soc., Providence (1999)
4. Bedford, E., Taylor, B.A.: The Dirichlet problem for a complex Monge–Ampère equation. Invent. Math. 37(1), 1–44 (1976)
5. Caffarelli, L., Kohn, J.J., Nirenberg, L., Spruck, J.: The Dirichlet problem for nonlinear second-order elliptic equations. II. Complex Monge–Ampère, and uniformly elliptic, equations. Commun. Pure Appl. Math. 38(2), 209–252 (1985)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献