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Results tagged with linear-pde
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user 150653
Questions about linear partial differential equations. Often used in combination with the top-level tag ap.analysis-of-pdes.
3
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Accepted
Schauder estimates with boundary conditions
The result is true. Let $L=\sum_{ij}a_{ij}D_{ij}$ and consider $$L^{-1}: C^{2+\alpha}(\partial \Omega) \mapsto C^{2+\alpha}(\bar \Omega)$$ with $L^{-1}f=u$ is $Lu=0$ and $u=f$ at the boundary.
$L^{-1} …
- 6,035
9
votes
Gradient $L^p$ estimates for heat equation
Let me comment on what I know in an open set $\Omega$, trying to control $C$. First of all, the heat semigroup can be expressed through a kernel $p$ which is pointwise dominated by the heat kernel in …
- 6,035