Timeline for How to deal with the boundary estimate for the Schauder estimates of laplacian equations?
Current License: CC BY-SA 4.0
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| Jul 10, 2023 at 4:29 | history | edited | Luis Yanka Annalisc | CC BY-SA 4.0 |
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| Oct 3, 2021 at 3:33 | comment | added | user378654 | The standard reference for regularity theory is Gilbarg, Trudinger, "Elliptic Partial Differential Equations of Second Order." | |
| Oct 3, 2021 at 3:33 | comment | added | user378654 | A common approach to boundary estimates is to flatten the boundary to a half-space by changing variables: this leads to an elliptic PDE with variable coefficients on, say, a half-ball. Then you proceed exactly as in the proof of interior Schauder estimates, except now using the constant-coefficient equation on a half-ball to approximate with. The constant-coefficient equation on a half-ball can studied using the Fourier transform, using the explicit form of the Poisson kernel, using reflection arguments, etc., there are many things that work. | |
| Oct 3, 2021 at 3:09 | history | edited | Luis Yanka Annalisc | CC BY-SA 4.0 |
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| Oct 3, 2021 at 3:03 | history | asked | Luis Yanka Annalisc | CC BY-SA 4.0 |