On the \(W^{2,1+\varepsilon }\)-estimates for the Monge-Ampère equation and related real analysis (Q2248842)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the \(W^{2,1+\varepsilon }\)-estimates for the Monge-Ampère equation and related real analysis |
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On the \(W^{2,1+\varepsilon }\)-estimates for the Monge-Ampère equation and related real analysis (English)
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27 June 2014
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The author is concerned with several qualitative results for the Monge-Ampère equation. One of the main results establishes a (1,2)-Poincaré inequality and a weak \((q,p)\)-Poincaré inequality associated to the Monge-Ampère quasi-metric structure. These results are applied to deduce a Harnack-type inequality for nonnegative solutions of the linearized Monge-Ampère equation. A key tool in the arguments throughout this paper are the \(W^{2,1+\varepsilon }\)-estimates for the Monge-Ampère equation.
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Monge-Ampère equation
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Harnack inequality
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Poincaré inequality
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