bio  website  math.poly.edu/~yang 

location  New York, New York  
age  
visits  member for  5 years, 2 months 
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stats  profile views  12,439 
4h

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Survey paper on isoperimetry
ams.org/journals/bull/19788406/S000299041978145534 
9h

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Why do we teach calculus students the derivative as a limit?
Ben, the ones who got it wrong just guessed that the derivative formulas would be the same for degrees as radians. The fact that they guessed instead of making some effort to work it out was in fact what flabbergasted me. I would also note that many (maybe most?) mathematicians are uncertain about whether the constant is $\pi/180$ or $180/\pi$. This is not such a serious issue, but it bothers me that any engineer or physicist would be able to answer instantly. 
2d

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Beginners Guide to Cartan for Beginners
There are other approaches to this theory. A modern cohomological approach was developed by Spencer, Quillen, Guillemin, Sternberg, and Goldschmidt. A nice description of an involutive first order differential operator was given by Guillemin and is now known as Guillemin normal form. Using this description, it is easy to construct examples of involutive systems of PDE's. Still another approach, using only basic linear algebra, is described in the first chapter of my thesis, "Involutive hyperbolic differential systems", Memoirs of the AMS. 
2d

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Beginners Guide to Cartan for Beginners
Your question is still too vague. A tableau is essentially a way to represent a constant coefficient first order system of PDE's. So any arbitrary system of first order PDE's gives you an example of a tableau. You can then test whether the tableau is in involution or not and prolong if necessary. You need to say more about what you're hoping to learn about in the examples. 
Dec 20 
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Beginners Guide to Cartan for Beginners
What's the question here? 
Dec 16 
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System of linear first order PDE with constant coefficients
Finally, if the system is degenerate, then you should post it here, and someone can help you figure out what, if any, compatibility conditions are needed. 
Dec 16 
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System of linear first order PDE with constant coefficients
You should check the references in the MO answer I linked to. They might handle the linear first order system case explicitly. Or you can compose your operator on the left by the cofactor matrix of your operator. This results in a higher order diagonal operator, which can then be analyzed using the results on higher order scalar operators. 
Dec 16 
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System of linear first order PDE with constant coefficients
A compatibility condition can arise only if the system is degenerate. The system is non degenerate if there exists a nonzero $(t_1, \dots, t_n)$ such that the matrix $t_1M_1 + \cdots + t_nM_n$ is invertible. If this holds, there are no compatibility conditions, and the system has a solution for suitable $b$. 
Dec 16 
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System of linear first order PDE with constant coefficients
You might try the answers to mathoverflow.net/questions/186779/… 
Dec 16 
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System of linear first order PDE with constant coefficients
Could you say on what domain you want a solution? A bounded domain, all of $\mathbb{R}^n$, in a neighborhood of a point, or something else? 
Dec 16 
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Moser's iteration for non homogeneous quasilinear elliptic PDE
And if you've spent many, many hours (or days) trying without success, you should post a more specific question explaining what you've been able to do so far and pointing out where you got stuck. 
Dec 16 
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Moser's iteration for non homogeneous quasilinear elliptic PDE
Usually, any technique for analyzing PDE's has to be adapted to a specific situation. You should learn how Moser iteration works in principle and see if you can use interpolation estimates (such as the GagliardoNirenberg inequalities) or whatever else you can find to make it work in this situation. 
Dec 14 
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The definition of $W_0^{1,\infty}$
And Lipschitz functions are continuous. 
Dec 14 
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The definition of $W_0^{1,\infty}$
For one thing $W^{1,\infty}_0 \subset W^{1,p}_0$ 
Dec 14 
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The definition of $W_0^{1,\infty}$
The answer is yes. And you still have trace equal to zero. 
Dec 14 
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The definition of $W_0^{1,\infty}$
You get Lipschitz functions. 
Dec 14 
reviewed  Close Interpolating (tangent)vectors on a sphere 
Dec 14 
reviewed  Close Time estimate to determine if a number is prime 
Dec 14 
reviewed  Close The singular value of $F(\theta)=\sin\theta\int_{a}^{a}e^{ikz\cos\theta}f(z)dz.$ 
Dec 14 
reviewed  Close On a paper by Yoneda 