Global \(W^{2,p}\) estimates for the Monge-Ampère equation (Q2845432)
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scientific article; zbMATH DE number 6203317
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global \(W^{2,p}\) estimates for the Monge-Ampère equation |
scientific article; zbMATH DE number 6203317 |
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30 August 2013
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Monge-Ampère equation
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global \(W^{2,p}\)-estimates
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localization method
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Global \(W^{2,p}\) estimates for the Monge-Ampère equation (English)
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In this paper, the author answers the natural question of whether the interior estimates can be extended up to the boundary for solutions to the Monge-Ampère equation. The main result establishes a global \(W^{2,p}\)-estimate under natural assumptions on the domain and boundary data. The proof is based on the localization theorem, which asserts that if the boundary data has a quadratic growth near \([x_n=0]\) then each section of the solution at the origin is equivalent to a half-ellipsoid centered at the origin.
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