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Results tagged with elliptic-pde
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user 91098
Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
4
votes
1
answer
52
views
Mapping properties of the Schrödinger semigroup
The Schrödinger semigroup $e^{t(-\Delta +V(x))}$ for Kato class potentials is fairly well-understood. A classical reference is the AMS paper "Schrödinger Semigroups" by Barry Simon. I was wondering wh …
- 1,045
8
votes
1
answer
341
views
Minimal assumptions such that the solution of Poisson equation is $C^2$
Take a weak solution $u$ of the Poisson equation on $\mathbb{R}^d$
$$ \Delta u = f $$
By standard elliptic regularity theory we have (for some $\alpha\in (0,1]$) $f\in C^{0, \alpha}_{\text{loc}}(\math …
- 17.2k