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Results tagged with reference-request
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user 51695
This tag is used if a reference is needed in a paper or textbook on a specific result.
4
votes
Accepted
Averaging the mass of a Sobolev function $f\in W^{1,p}(\Omega)$ near $\partial\Omega$
In Evans & Gariepy's "Measure theory and fine properties of functions", Sec. 5.3., they construct the trace operator on a bounded Lipschitz domain $\Omega$ for BV-functions (and thus by inclusion for …
- 2,504
3
votes
Accepted
Fast algorithms for calculating the distance between measures on finite ultrametric spaces
This is a rather more fun problem than I thought. I must apologize though, as your question is a reference request and I have no references apart from pointing at any textbook on discrete optimization …
- 2,504
1
vote
Accepted
Isoperimetric inequality for exterior domains on $\mathbb{H}^{n}$
I might be missing something, but if you require $\Omega$ to be precompact in $\mathbb{H}^n \setminus K$, then $K$ makes no difference for the purpose of determining the measures and you can use the o …
- 2,504
1
vote
Accepted
Non convex optimization problem in $W_0^{1,2}$
You can treat this as a problem with two Lagrange multipliers. Then by standard methods, a minimizer $f$ has to exist (by convexity in $f'$) and has to be a weak solution to
$$-f'' + \lambda f + \mu f …
- 2,504
1
vote
0
answers
12
views
On the relation between quasiconvex functionals and quasimonotone operators
The following is a classical definition due to Morrey: Let $\Omega \subset \mathbb{R}^n$ be a nice enough, bounded domain and $f: \mathbb{R}^{m \times n} \to \mathbb{R}$ with some reasonable growth co …
- 2,504