Interior curvature bounds for a class of curvature equations. (English) Zbl 1174.35378
In the present study the authors derive interior curvature bounds for admissible solutions of a class of curvature equations subject to affine Dirichlet data, generalizing the well-known interior second derivative bound for equations of Monge-Ampère type. In addition, in the case where convexity of the solution is the natural ellipticity assumption, the authors prove an interior curvature bound for convex solutions subject to \(C^{1,1}\) data. Moreover, they use the curvature bound to extend and to improve various existence results for the Dirichlet and Plateau problems.
Reviewer: Messoud A. Efendiev (Berlin)
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35B45 | A priori estimates in context of PDEs |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
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