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Results tagged with reference-request
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user 76318
This tag is used if a reference is needed in a paper or textbook on a specific result.
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Isomorphism between Sobolev space and its dual for elliptic system
Given a domain $\Omega\subset\mathbb{R}^d$, suppose that the boundary is sufficiently regular. Then by Gröger's regularity theory we know that the following operator
\begin{equation}
\nabla\cdot\nabla …
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Examples for differential operators first order
Currently I am dealing with the problems which involve the general first order differential operator, i.e., for some open domain $\Omega\subset\mathbb{R}^n$ with certain regular bondary and a function …
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Sobolev regularity for systems of elliptic boundary value problems
I think the reason that you can hardly find reference about the vector valued functions is that you can always reduce your situation to scalar ones, since you can always use test function such that it …
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Browder's Fixed Point Theorem in uniformly convex Banach spaces with non-identical image
This is in fact an exercise from Dirk Werner's book "Funktionalanalysis", but I do think that the result is quite interesting and up to now, I can only partly solve this problem. From the point of my …
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Asking for Advices for Choosing a Ph.D thesis problem (in PDE area)
I'm a first year phd student in Germany. I've started my phd study one year ago and I'm currently confused about the topic I've chosen. The program is in the area of PDEs, and actually I didn't learn …
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