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May
22
comment How to understand a proposition of subgradient
This result just says that on the relative interior of the domain the values of the subdifferential are non-empty compact convex up to the added orthogonal of the affine hull of the domain. This is a structure result.
May
20
answered Prove that for any positive integer $n$, $A^n ≠ I$.
May
19
comment Proving that $\text{ri rge}\,A=\text{ri conv rge}\,A$
@copper.hat You clearly misunderstood. I am interested only in Math.
May
19
comment Compute flux of vector field F through hemisphere
You need to know how to compute surface integrals when your surface is given parametrically (you need use spherical coordinates) or explicitly and afterward you need pick the right normal vector.
May
19
comment Proving that $\text{ri rge}\,A=\text{ri conv rge}\,A$
@copper.hat It seems that you like the subject. So how would you prove that cl rge A is convex? (That is part of this post) Crucial and most are very relative words. And I believe that here ri can mean even the relative algebraic interior. Your thoughts on that?
May
19
comment Proving that $\text{ri rge}\,A=\text{ri conv rge}\,A$
@copper.hat You put the same answer long after I posted my answer (timewise) but on the page it shows "before" my answer. I hope you understand now. As I explained before yes the relation does follow from applying ri while the rest of the details must be found by the person who posted it. An answer should not contain all details especially when the author of the post makes no effort towards solving it or takes an idea from a comment and writes another post. I don't know anything about your diapers or my high horses and as promised this is my last comment here.
May
19
comment Proving that $\text{ri rge}\,A=\text{ri conv rge}\,A$
@copper.hat My answer is correct. And the details you cannot explain for yourselves are a good exercise for both of you. It is also extremely annoying that you post the same proof as a comment before my answer. I assume that you finally understood the proof. (Yes the final explanation that you both should have found is that the affine hull the ri conv rge A equals the affine hull of (conv) rge A.) None of your comments told me anything new. If you want to argue about the validity of the proof I am happy to talk. Otherwise I will try to refrain from answering such posts.
May
17
answered Proving that $\text{ri rge}\,A=\text{ri conv rge}\,A$
Apr
11
awarded  Mortarboard
Apr
7
comment Fake proof: Equivalence of norms
$\mu$ depends on $f$ while $\alpha$ should not depend on $f$ but it does if you want to fulfill your last inequality.
Apr
5
answered (Updated) Geometric Illustration of Monotone and Maximal Monotone Maps
Apr
5
comment (Updated) Geometric Illustration of Monotone and Maximal Monotone Maps
You need to be more specific. What is a "geometric illustration" as well as an "excellent example" for you? You want only maximal monotone operators in finite dimensions? The literature on maximal monotone operators is extremely broad.
Mar
12
comment arclength parametrization intuition
The speed of drawing the curve in the standard parametrization is $1$.
Mar
7
answered Why is $(T + N_X)(x) \subset T(x)$ when $Dom T \subset X$?
Mar
6
comment Closure of the interior of the epigraph
Yes, the closure of the non-empty interior of a closed convex set is the set itself in any linear topological space. You can find this result in Holmes: "Geometric Functional Analysis and its Applications" on p. 59 and its proof is based on the continuity of the operations.
Feb
18
answered Non-linear analysis
Feb
17
revised Example of maximal monotone operators in non-reflexive Banach spaces with applications in PDE
added 100 characters in body
Feb
12
comment Example of maximal monotone operators in non-reflexive Banach spaces with applications in PDE
Of course any subdifferential is maximal monotone and is involved in variational inequalities (in any Banach space). What about examples that do not depend on the subdifferential?
Feb
12
asked Example of maximal monotone operators in non-reflexive Banach spaces with applications in PDE
Feb
6
revised Continuity of the dual product reloaded
deleted 21 characters in body