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\(C^{2,\alpha }\) estimates for nonlinear elliptic equations of twisted type

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Abstract

We prove a priori interior \(C^{2,\alpha }\) estimates for solutions of fully nonlinear elliptic equations of twisted type. For example, our estimates apply to equations of the type convex + concave. These results are particularly well suited to equations arising from elliptic regularization. As application, we obtain a new proof of an estimate of Streets and Warren on the twisted real Monge–Ampère equation.

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Acknowledgments

I would like to thank G. Székelyhidi, V. Tosatti and C. Mooney for several helpful conversations. I am grateful to D. H. Phong and S.-T. Yau for their encouragement and support. I am particularly grateful to the referee for several suggestions which helped to improve and clarify the content of this paper.

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  1. Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA, 02138, USA

    Tristan C. Collins

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  1. Tristan C. Collins
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Correspondence to Tristan C. Collins.

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Communicated by O. Savin.

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Collins, T.C. \(C^{2,\alpha }\) estimates for nonlinear elliptic equations of twisted type. Calc. Var. 55, 6 (2016). https://doi.org/10.1007/s00526-015-0950-y

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