The weighted reverse Poincaré type inequality for the difference of two parabolic subsolutions (Q2836173)
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scientific article; zbMATH DE number 6662119
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The weighted reverse Poincaré type inequality for the difference of two parabolic subsolutions |
scientific article; zbMATH DE number 6662119 |
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7 December 2016
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weak parabolic subsolutions
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reverse Poincaré inequality
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gradient of the subsolution
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The weighted reverse Poincaré type inequality for the difference of two parabolic subsolutions (English)
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This paper proves a weighted estimate for a difference of two continuous weak subsolutions of linear uniformly parabolic second order partial differential equations with constant coefficients in cylindrical domains. The main result gives an estimate to the \(L^2\) norm of the difference of the gradients in terms of the \(L^\infty \) norm of the difference of the subsolutions. The estimate is first proved for smooth subsolutions and the general result is obtained by an approximation procedure.
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0.7820804715156555
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0.7667009830474854
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