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Results tagged with fa.functional-analysis
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user 111925
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
1
answer
295
views
Is there a name for the space of gradients?
Let $\Omega \subseteq \mathbb{R}^n$ be a bounded domain. Define the set
$$H = \left\{\nabla f : f \in \mathcal{C}^1(\Omega)\right\}.$$
I suspect that $H$ is a Hilbert space (though I am unsure about c …
- 45
2
votes
1
answer
396
views
Second-order elliptic regularity with rough coefficients
Let $\Omega \subseteq \mathbb R^n$ be a bounded open set with smooth boundary. Let $k\geq 1$, $\alpha\in(0,1)$, $a_{ij},b_i,f \in C^{k,\alpha}(\Omega)$ for $i,j=1,...,n$, and define the operator
$$L = …
- 45