2016
DOI: 10.1007/s00526-015-0950-y
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$$C^{2,\alpha }$$ C 2 , α estimates for nonlinear elliptic equations of twisted type

Abstract: We prove a priori interior C 2,α 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-Warren [18] on the twisted real Monge-Ampère equation.

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Cited by 16 publications
(6 citation statements)
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“…Proof. The proof is by a standard blow-up argument; see, for instance [9]. We give the details for the convenience of the reader.…”
Section: Higher Order Estimatesmentioning
confidence: 99%
“…Proof. The proof is by a standard blow-up argument; see, for instance [9]. We give the details for the convenience of the reader.…”
Section: Higher Order Estimatesmentioning
confidence: 99%
“…If the linearized operator for F satisfies a Cordes-Nirenberg condition, one can also obtain this boosting (see Section 5). Since the 1980s, it has been a challenge to find equations with the regularity boosting property that are niether convex nor concave, see for example [CY00], [Yua01], [CC03] , [Col16], [SW16], [Pin16]. Savin [Sav07] proved interior C 2,α (and higher) estimates for viscosity solutions of (1.2) that are sufficiently close to a quadratic polynomial, for F smooth.…”
Section: Introductionmentioning
confidence: 99%
“…A similar problem is examined in [11]. In that paper, the author produces a priori estimates for the solutions to…”
Section: Introductionmentioning
confidence: 99%