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Results tagged with elliptic-pde
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user 62739
Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
0
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207
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Distance function to the boundary and Harnack inequality
Suppose $\Omega \subset \mathbb{R}^d$ be a domain, and let $\rho(x) = \mathrm{dist} (x, \partial \Omega)$ be the distance function to the boundary of $\Omega$. I want to know for which domains $\rho$ …
- 747
4
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2
answers
514
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The solution of Poisson equation and the distance function from the boundary
Let $D$ be a domain in $\mathbb{R}^n$, and let $u$ be the solution to the Poisson equation, that is
$$ \begin{cases}
\Delta u = f & \text{in} ~ D, \\
…
- 747
3
votes
0
answers
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Singular integral operators and PDEs
What is the relation between the notion of singular integral operators and partial differential equations?
I know, for example, that there is a relation between the Cauchy transform (Riesz transforms …
- 747