bio  website  math.poly.edu/~yang 

location  New York, New York  
age  
visits  member for  5 years, 5 months 
seen  24 mins ago  
stats  profile views  13,052 
1h

comment 
freedom in choosing a smooth function of compact support
This is not appropriate for this site. Besides have you tried this when $n=1$? 
18h

comment 
Derivative of Log_p map
The inverse of the derivative of the exponential map. 
2d

comment 
Differential forms along the fiber
Another way to say what user74230 said is that given a subspace $W\subset V$ let $W^\perp \subset V$ be its annihilator. Then $W^* = V^*/W^\perp$. Therefore, at each point $p$ in the bundle $E$, $k$forms on the fiber are given by $\Lambda^kT^*_pF = \Lambda^k(T^*_pE/(T_pF)^\perp).$ In particular, no connection is needed. 
Mar 24 
awarded  Nice Answer 
Mar 24 
comment 
Are linearizations of involutive PDEs locally solvable?
The step in the CartanKahler theorem that I didn't find obvious is the dimension of the space of formal 2nd order solutions to the linearized system. The last paragraph of my answer shows how to get this from the involutivity of the nonlinear system. 
Mar 23 
comment 
Are linearizations of involutive PDEs locally solvable?
The inhomogeneous case requires only that the inhomogeneous term satisfy compatibility conditions, which are equivalent to saying that the system has at least one formal 2nd order solution. 
Mar 23 
comment 
Are linearizations of involutive PDEs locally solvable?
Unfortunately, by now I find my own monograph unreadable. 
Mar 23 
revised 
Are linearizations of involutive PDEs locally solvable?
added 22 characters in body 
Mar 23 
revised 
Are linearizations of involutive PDEs locally solvable?
added 1349 characters in body 
Mar 23 
comment 
Are linearizations of involutive PDEs locally solvable?
I see that you're a graduate student at Minnesota. Surely, Peter Olver would know the answer to this? 
Mar 23 
answered  Are linearizations of involutive PDEs locally solvable? 
Mar 22 
comment 
Sobolev space for manifold with boundary
It's best to fix boundary conditions such as Dirichlet or Neumann boundary conditions. 
Mar 18 
comment 
Schauder estimate on a bounded domain
guacho appears to be right about this. You can only get a bound of the extension in terms of the full Sobolev norm of the original function. 
Mar 18 
comment 
Schauder estimate on a bounded domain
You have to estimate the commutator of the extension operator and partial differentiation. I suggest looking at the extension operator defined in Stein's book, Singular Integrals and Differentiability Properties of Functions. 
Mar 17 
awarded  Guru 
Mar 16 
comment 
explicit solution to linear PDE — boundary value problem
This is not a research level question. I suggest posting the question either on math.stackexchange.com or www.reddit.com/r/math 
Mar 15 
awarded  Good Answer 
Mar 14 
awarded  Nice Answer 
Mar 14 
comment 
Parodies of abstruse mathematical writing
Nate, many thanks for the edit! It's much better answer now. I'm sorry for posting my answer before you could. 
Mar 14 
answered  Parodies of abstruse mathematical writing 