Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second order estimates for Hessian type fully nonlinear elliptic
  equations on Riemannian manifolds   We derive a priori estimates for second order derivatives of solutions to a
wide calss of fully nonlinear elliptic equations on Riemannian manifolds. The
equations we consider naturally appear in geometric problems and other
applications such as optimal transportation. There are some fundamental
assumptions in the literature to ensure the equations to be elliptic and that
one can apply Evans-Krylov theorem once estimates up to second derivatives are
derived. However, in previous work one needed extra assumptions which are more
technical in nature to overcome various difficulties. In this paper we are able
to remove most of these technical assumptions. Indeed, we derive the estimates
under conditions which are almost optimal, and prove existence results for the
Dirichlet problem which are new even for bounded domains in Euclidean space.
Moreover, our methods can be applied to other types of nonlinear elliptic and
parabolic equations, including those on complex manifolds.

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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int