# Tagged Questions

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### Discrete Poincare Inequality

For the sake of this question, let $\Omega \subset \mathbb{R^2}$ be a regular domain. In variational problems involving the Sobolev space $W^{1,1}(\Omega)$ (or $BV(\Omega)$) one often uses the Sobolev ...
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### dual of $H^1_0$: $H^{-1}$ or $H_0^1$?

I have a problem related to dual of Sobolev space $H^1_0$. By definition, the dual of $H^1_0$ is $H^{-1}$, which contains $L^2$ as a subspace. However, from Riesz representation theorem, dual of a ...
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### Density of smooth functions in fractional Sobolev space

I am reading a paper on the analysis of numerical methods, and am confused about a statement made. I am working in fractional Hilbert spaces, but I don't think that this has much bearing on the answer ...
### $H^1$ estimate by $L^2$-norm
Let $(\tau_h)$ be a shape regular triangulation. Prove that there exists a constant $c>0$ such that $$\|v\|_{H^1(\Omega)}\leq \frac{c}{\min_{T\in\tau_h}} \|v\|_{L^2(\Omega)}$$ for all $v\in V^h$ ...