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Results tagged with regularity
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user 13093
regularity of solutions of PDEs.
0
votes
1
answer
543
views
A property of sets of finite perimeter
I have a question regarding sets of finite perimeter. I feel that it should be true, but I didn't manage to prove or find a reference about it. Suppose $D$ is an open, bounded subset of $\Bbb{R}^n$, a …
- 2,222
1
vote
Accepted
A property of sets of finite perimeter
I'm sorry that I answer my own question, but I found out the answer this morning from my teacher. There are examples of sets of finite perimeter with positive measure, which do not contain any open ba …
- 2,222
3
votes
3
answers
2k
views
Does regularity of the boundary imply interior sphere condition
In the article of Massari presented here there is a trace inequality which is said to be true for domains which satisfy the interior sphere condition:
There exists $\rho>0$ such that for every $x …
- 2,222
1
vote
1
answer
47
views
Approximation with a more regular function and an inequality constraint
The motivation of the question comes from a geometric problem: can we approximate a $C^{1,\alpha}$ set $\Omega$ with positive curvature (in distributional sense) from inside with $C^2$ sets with posit …
- 2,222
0
votes
Accepted
Approximation with a more regular function and an inequality constraint
Looks like the answer to this question is affirmative. In fact the question is equivalent to the following one: Regularization by mean curvature flow
Take a look at the article in the given answer …
- 2,222
1
vote
Regularity - mean curvature equation
This question is solved in the PhD thesis of Nicolas Landais: Problèmes de régularité en optimisation de forme. You can read the thesis here. The result is presented in Chapter 6. The conclusion is th …
- 2,222