bio | website | regularize.wordpress.com |
---|---|---|
location | Braunschweig, Germany | |
age | 36 | |
visits | member for | 4 years |
seen | 13 hours ago | |
stats | profile views | 1,706 |
Professor at TU Braunschweig.
Area: Inverse problems, regularization theory, applied functional analysis, mathematical image processing.
Jun 16 |
comment |
Extension operator for Lipschitz domain for fractional Sobolev spaces
The boundary regularity needed is $C^{m,1}$ for an extension of an $H^{s,p}$-function with $0\leq s\leq m+1$. Hence Lipschitz works for $0\leq s\leq 1$. This is similar to what Dobrowolski proves for the integrer case in Satz 6.11. However, I just had a breif view on Stein's result and he seems to use a very different technique and only needs Lipschitz for arbitrary high $m$, right? |
Jun 15 |
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Extension operator for Lipschitz domain for fractional Sobolev spaces
I think the answer is yes and stated in Satz 6.40 in "Angewandte Funtionalanalysis" by M. Dobrowolski (but unfortunately in German). As far as I have seen, the proof imitates the one for the integer case: First provide estimates for the extension from a half space to the whole space and then use localization and Lipschitz-continuous deformation. |
Jun 10 |
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Distributing points with respect to a concave function
Did you try to minimize $F$, e.g. by calculating its (sub-)derivatives with respect to all coordinates $x_i$ all solving the resulting equations? |
May 5 |
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Floquet transform of the derivative of a function
Since Answers should be answers to the original question, this should have been a comment to Carlo's answer... |
May 2 |
awarded | Nice Answer |
Apr 29 |
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Is there an integration free proof (or heuristic) that once differentiable implies twice differentiable for complex functions?
Thanks for fixing the links, jc! Since this always happens to my links, it seems that I have a problem with the encoding... |
Apr 29 |
answered | Is there an integration free proof (or heuristic) that once differentiable implies twice differentiable for complex functions? |
Apr 26 |
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Resources for mathematics advising.
+1 for pointing out the Rumsfeldian unknown unknows (some of which I know very well...). |
Apr 6 |
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What is the “correct” generalization of operator norms for nonlinear operators?
Usually a norm is used to turn a vector space into a normed space. Do you have a special vector space of nonlinear operators in mind? Probably the space of all nonlinear operators between two (normed?) spaces is too large... |
Apr 5 |
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Elementary+Short+Useful
Thanks! Link Corrected. |
Apr 5 |
revised |
Elementary+Short+Useful
Corrected link |
Apr 5 |
awarded | Nice Answer |
Apr 3 |
answered | Elementary+Short+Useful |
Mar 31 |
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FEM on a Laplacian
Well, that way you need one order of differentiability less for $u$ which allows rougher elements. Moreover, since integration by parts holds, both left hand sides are the same and not doing it will lead to the same linear system (if $u$ or its ansatz functions are regular enough). |
Mar 19 |
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What are your favorite instructional counterexamples?
Yeah, that works, too! However, I experienced that undergraduates sometimes feel a bit uncomfortable with such "piecewise" definitions and are more happy with a more "natural" example (whatever that means). |
Mar 17 |
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When does symmetry in an optimization problem imply that all variables are equal at optimality?
Maybe I just illustrate with your example: The symmetry you had in your question is the symmtery under the action of the permutation group. The optimization variable is $(x,y)$ and the objective $f(x,y) =x+y$ does not change under the mapping $P(x,y)= (y,x)$, i.e. $f(x,y) = f(y,x)$. Moreover, the mapping $P$ maps the feasibile region $x^2+y^2\geq 1$, $x,y\geq 0$ one-to-one and onto itself. Consequently, if $(x^*,y^*)$ is a solution, $P(x^*,y^*) = (y^*,x^*)$ also is. |
Mar 17 |
awarded | Necromancer |
Mar 17 |
answered | When does symmetry in an optimization problem imply that all variables are equal at optimality? |
Feb 25 |
answered | Applications of mathematics |
Feb 15 |
awarded | Enthusiast |