Delio Mugnolo
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Registered User
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1d |
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Does this qualify as “self plagiarism” or something? @Vidit Nanda I do not believe that quoting an older paper for its notation is any better than copying and pasting its content to the new one. A reader might easily conclude that one is simply trying to increase her/his own h-index... |
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May 8 |
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radon-nikodým property of $\ell^\infty$ ok, now I understand. |
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May 8 |
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radon-nikodým property of $\ell^\infty$ András, I do not understand this comment, either. This shows that $\ell^1$ has the R-N property, of course. But why does anything about $\ell^\infty$, or weighted version thereof, follow? |
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May 8 |
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radon-nikodým property of $\ell^\infty$ András, I am not sure I understand. That Proposition is about $c_0$, right? |
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May 8 |
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radon-nikodým property of $\ell^\infty$ chosed a more appropriate title |
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May 7 |
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radon-nikodým property of $\ell^\infty$ Uh, thanks a lot. I found exactly the same answer simultaneously. I am not familiar with the theory of Asplund spaces, so why is $\ell^1$ "obviously" no Asplund space? For the reason I mention or is there some simpler explanation? |
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May 7 |
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radon-nikodým property of $\ell^\infty$ problem seems now to be solved |
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May 7 |
asked | radon-nikodým property of $\ell^\infty$ |
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Apr 21 |
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Is this a Banach space? Is your $H^2$ the same as $H^2(\mathbb R^3)$? If so, and due to uniqueness of your decomposition, is $Q$ not always 0 and $\phi=u$? |
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Apr 12 |
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Mathematical “urban legends” well, and in large parts of the rest of europe, too. |
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Mar 26 |
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projection of sobolev spaces onto cones thanks. i do not yet see why you write "hence, there is no easy formula" - several special solutions of complicated nonlinear pdes are known, and of course that minimum is the inf of an lsc functional (perhaps even smoother), but i do agree that "morally" this will be hard. |
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Mar 25 |
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projection of sobolev spaces onto cones btw, i know too little of calculus of variations to appreciate your reference to the obstacle problem. i guess that what you call the "obstacle problem" (or a solution thereof) is simply the abstract formula which in functional analysis is used to characterize the orthogonal projection. but of course this characterization is in general purely abstract, that is, you come nowhere close to an explicit expression. |
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Mar 25 |
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projection of sobolev spaces onto cones gerw, thanks for your answer/comment. sure, i can take the vector with smallest distance. the problem is that i'd like to have an explicit, analytic expression of how this element of minimal distance look like. let me be more explicit: if we were in $L^2$, and not in $H^1$, then for all $f\in L^2$ its orthogonal projection onto the cone of positive-valued $L^2$-functions would be simply $f^+$, the positive part of $f$: that is, the pointwise maximum between $f(x)$ and $0$ (a.e.). but i have no idea how an analogous formula could look like, if one considers the $W^{1,2}$-distance instead. |
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Mar 25 |
accepted | H_0^1 and C_infinity on the interior, does that imply classical limit is 0 on the boundary? |
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Mar 24 |
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H_0^1 and C_infinity on the interior, does that imply classical limit is 0 on the boundary? Sorry, I just realized that there is a bug (?) in MO-code so that it will accept \bar but not \overline. This induced a wrong version of Brezis' result. You can now see the actual version. Concerning your new question: Your setting should be formulated in a more precise way (what kind of elliptic problem are you thinking of?) Anyway, relatively mild assumptions imply that the solution is in $C^2(\bar{\Omega}$, cf.Thm. 9.25 in Brezis. (Btw: for better later readability you should in the future highlight your edits, otherwise the first answers might look bizarre/off-topic/wrong afterwards) |
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Mar 24 |
revised |
H_0^1 and C_infinity on the interior, does that imply classical limit is 0 on the boundary? deleted 5 characters in body |
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Mar 21 |
accepted | What are some interesting almost equitable partitions which are not equitable? |
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Mar 21 |
revised |
H_0^1 and C_infinity on the interior, does that imply classical limit is 0 on the boundary? added 10 characters in body |
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Mar 21 |
answered | H_0^1 and C_infinity on the interior, does that imply classical limit is 0 on the boundary? |
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Mar 21 |
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Functional Analysis Generalizations: indeterminated inner product and functions over manifolds I guess what you are looking for are Krein spaces and their (better behaved) special cases, Pontryagin spaces. Heinz Langer and his school have worked a lot on them. |
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Mar 19 |
answered | Manifold-Valued Sobolev Spaces |
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Mar 19 |
asked | projection of sobolev spaces onto cones |
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Mar 17 |
awarded | ● Enthusiast |
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Mar 16 |
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Doubt on norm of the Sobolev space $H^2(\mathbb{R}^3)$ Peter Michor's suggestion is correct, but you might want to check Gårding's inequality for a possibly even easier argument. |
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Mar 16 |
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How does hyperbolicity of space time affect our lives? Ben Crowell, I am not quite sure the two ways of using that world are actually unrelated. The solvability features of a wave equation (as opposed to, say, a heat equation) actually depend on the fact that the "hyperbolic" wave equation is a PDE whose symbol is a function with certain properties - the same properties that one would need to define a riemannian metric of negative curvature. |
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Mar 16 |
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Is this function in the weighted Sobolev space $H^{2,-s}$? Another non-mathematical suggestion: It seems that you have split a certain somewhat substantial mathematical problem into tiny pieces and keep on posting asking for solutions of these sub-problems. I doubt this is the most efficient way of solving your problem, and not necessarily the fairest way of dealing with other MO-users, either. Besides: some of your questions really are terribly technical and not really of large interest. |
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Mar 12 |
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origin of the notion of “network” in graph theory typo |
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Mar 12 |
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Limit of a function in a weighted Sobolev space Yes, so I believe. |
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Mar 12 |
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Limit of a function in a weighted Sobolev space The same used here en.wikipedia.org/wiki/Sobolev_inequality , from where I've taken the second embedding (I can never remember the embeddings by heart). |
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Mar 12 |
answered | Limit of a function in a weighted Sobolev space |
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Mar 12 |
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Applications of line graphs say, this: wisdomofwhores.com/wp-content/uploads/2010/12/… or this: asu.edu/clas/csdc/events/pdf/moody.pdf |
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Mar 12 |
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origin of the notion of “network” in graph theory Ok, I was not aware of this. I thought the definition of "network" was well-established in graph theory - I have found it in almost all textbooks. But ok, then I am actually addressing the question you mean. |
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Mar 11 |
asked | origin of the notion of “network” in graph theory |
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Mar 11 |
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how do I withdraw my submitted paper? but why don't you send the correct version to the same journal, if I may ask? |
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Mar 10 |
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Eigenfunctions of elliptic operator form an orthonormal basis for L_2? John, beware that by definition $L^2(0,1)=L^2[0,1]$, as $[0,1]\setminus(0,1)$ is a set of zero Lebesgue measure. |
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Mar 9 |
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Eigenfunctions of elliptic operator form an orthonormal basis for L_2? nobody says that the decomposition should be finite. try integrating your function against the eigenfunctions, use thse so-called fourier coefficients $a_n$ to define the series $\sum_{n\in \mathbb N}a_n e_n$, and take a look at its limit in the $L^2$-norm. |
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Mar 9 |
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Every function in W^{1,1}(0,1) is continuous on (0,1) that's it. it could be additionally mentioned that $W^{1,1}$-functions are also absolutely continuous. |
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Mar 7 |
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Applications of line graphs That's exactly what I do not want, Jernej :) Of course, most of the graphs are already line graphs of some other graphs. Mine is not a mathematical question: it is, if you wish, an epistemological question. When do people working in other fields feel the need to introduce the (slightly non-standard, in their eyes) line-graph-based paradigm? All the examples of applications of graphs I'm aware of do not (at least not those in the soft sciences) make any use of graph theory, let alone applying theorems on coloring of graphs. Harary's sociological papers were a luminous exception, of course |
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Mar 7 |
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N-laplacian and Kelvin transform Is it a conjecture, you have read it somewhere and you cannot remember, is it a hope? The Kelvin transform itself does not depend on an operator, so I guess you actually refer to the result stating equivalence of (super/sub)harmonicity of some function and of its Kelvin transform. Do you expect exactly the same result? And - most importantly: why do you refer to the case of $p=n$ as "the borderline case"? The above result holds for the (2-)Laplacian regardless of dimension! |
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Mar 7 |
asked | Applications of line graphs |
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Mar 6 |
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existence of a minimum for a convex functional on a non-reflexive space it is continuous if the graph is uniformly locally finite, which is not optimal, but still ok. does the proof you mentioned above use the fact that $\ell^1$ is a separable dual space, then, or it is based on completely different ideas? |
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Mar 6 |
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Compactness of Sobolev embedding for domains of finite measure (say, to get extactly that extension Brezis needs a $C^1$ boundary in his book, and his proof is still not straightforward). |
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Mar 6 |
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existence of a minimum for a convex functional on a non-reflexive space It's a 1-Dirichlet functional, meaning $$f\mapsto \|I^T f\|_\{\ell^1},$$ where $I$ is the incidence matrix of a graph. |
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Mar 6 |
asked | existence of a minimum for a convex functional on a non-reflexive space |
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Mar 6 |
revised |
Interior regularity for elliptic equations improved formatting |
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Mar 5 |
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Compactness of Sobolev embedding for domains of finite measure @Daniel I am not sure that you can extend a $H^1$-function defined on a domain that is arbitrarily ugly to another $H^1$-function defined in the whole space, or in a ball. (Indeed, extending the given function in a reasonable way is exactly the main difficulty in proving compactness results). |
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Mar 4 |
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Eigenvalues of directed Laplacian matrix $L$ and $DL$, where $D$ is a diagonal matrix with positive entries Isn't that paper on graphs - as opposed to digraphs? |
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Mar 3 |
answered | Compactness of Sobolev embedding for domains of finite measure |
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Feb 28 |
revised |
power bounded adjacency matrices restricted the question to digraphs |
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Feb 27 |
revised |
power bounded adjacency matrices added 24 characters in body; added 59 characters in body |
