Second derivative estimates for uniformly elliptic operators on Riemannian manifolds (Q468631)
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scientific article; zbMATH DE number 6366907
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Second derivative estimates for uniformly elliptic operators on Riemannian manifolds |
scientific article; zbMATH DE number 6366907 |
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Second derivative estimates for uniformly elliptic operators on Riemannian manifolds (English)
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7 November 2014
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fully nonlinear elliptic equation
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Riemannian manifold
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\(W^{2,\varepsilon}\)-estimates
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ABP method
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The author obtains a uniform \(W^{2,\varepsilon}\)-estimate for solutions of the fully nonlinear uniformly elliptic equation NEWLINE\[NEWLINE F(D^2u,x)=f(x)\quad \text{in}\;B_R(z_0)\subset M, NEWLINE\]NEWLINE where \(M\) is a Riemannian manifold with lower bound for the sectional curvature. The approach relies on the Aleksandrov-Bakelman-Pucci method.
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