14,538 reputation
147112
bio website math.poly.edu/~yang
location New York, New York
age
visits member for 5 years, 5 months
seen 3 hours ago

Mar
28
comment freedom in choosing a smooth function of compact support
This is not appropriate for this site. Besides have you tried this when $n=1$?
Mar
28
comment Derivative of Log_p map
The inverse of the derivative of the exponential map.
Mar
26
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 Cartan-Kahler 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