14,363 reputation
144106
bio website math.poly.edu/~yang
location New York, New York
age
visits member for 5 years, 2 months
seen 7 mins ago

2d
comment 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.
2d
comment 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.
2d
comment 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 $b$.
2d
comment System of linear first order PDE with constant coefficients
You might try the answers to mathoverflow.net/questions/186779/…
2d
comment 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?
2d
comment 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.
2d
comment 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 Gagliardo-Nirenberg inequalities) or whatever else you can find to make it work in this situation.
Dec
14
comment The definition of $W_0^{1,\infty}$
And Lipschitz functions are continuous.
Dec
14
comment The definition of $W_0^{1,\infty}$
For one thing $W^{1,\infty}_0 \subset W^{1,p}_0$
Dec
14
comment The definition of $W_0^{1,\infty}$
The answer is yes. And you still have trace equal to zero.
Dec
14
comment 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
Dec
13
reviewed Close Continuously dependent on parameters
Dec
13
reviewed Close second fundamental form of boundary of convex subset non-negative?
Dec
12
comment $\lVert u\rVert_{W^{2,p}}$ is bounded above by $\lVert \Delta_p u\rVert_{L^2}$ for $u \in W^{1,p}_0 \cap W^{2,p}$?
The question assumes the function is compactly supported, so boundary regularity is not an issue.
Dec
11
comment Uhlenbeck's theorem novelty
I'm sure there are other references by now, but one is Instantons and Four-Manifolds. by Freed and Uhlenbeck.
Dec
11
comment A sum-of-determinants identity
It's disappointing that you didn't get a quick answer on math.stackexchange.com.