8,457 reputation
12772
bio website people.epfl.ch/willie.wong
location Lausanne, Switzerland
age 31
visits member for 4 years, 7 months
seen 12 hours ago
PostDoc at the PDE group at EPFL. I tend to like working with evolution equations from general relativity and Lagrangian field theories.

13h
comment Hardy-type inequality for point boundary
There seems to be some formatting problems with the last paragraph.
15h
reviewed Edit Finding the source for minimizer of a functional for all $C^2$-curve $x(t_0)=x_0$ and $x(t_1)=x_1$
15h
revised Finding the source for minimizer of a functional for all $C^2$-curve $x(t_0)=x_0$ and $x(t_1)=x_1$
added 21 characters in body; edited tags
16h
comment Inverse of partial differential operator as a smooth tame map
Thank you for the very nice reference.
19h
comment Inverse of partial differential operator as a smooth tame map
Do you know somewhere Qi's result is described or reproduced? The Acta Math. Sin. website does not have the full text for that issue (actamath.com/Jwk_sxxb_cn/CN/volumn/volumn_1770_abs.shtml)
19h
revised Hardy-type inequality for point boundary
removed real analysis (since subsumed by CA) and added AP because it is something that PDE people would likely know about.
19h
reviewed Leave Closed Generate Gamma random number using scale or rate parameters
19h
comment Period doubling bifurcation curve
Ok, now it is clear what you are asking. I remove my previous comments and vote to re-open.
20h
reviewed Reopen Period doubling bifurcation curve
20h
comment numerical method (implicit) for nonlinear pde
I still don't see the point of the formula for $\lambda(t)$. Isn't $\lambda$ an independent variable in the PDE? Why are you giving a formula for $\lambda$? Also, your first and third boundary conditions are incompatible.
20h
comment “Integrating” solenoidal vector fields
For smooth boundaries, possibly yes, in some advanced calculus textbooks. For Lipschitz boundaries I am slightly doubtful.
1d
comment “Integrating” solenoidal vector fields
You are describing basically the Hodge decomposition. For Lipschitz domains the result is derived in this AMS memoir (and probably elsewhere too).
1d
reviewed Reviewed Period doubling bifurcation curve
1d
reviewed Close Examples of intuition from fields other than Physics to solve math problems
2d
reviewed Close Decay of weak solutions to degenerate parabolic PDEs on manifolds without boundary
2d
comment Decay of weak solutions to degenerate parabolic PDEs on manifolds without boundary
On a compact manifold without boundary, $u \equiv 1$ is a solution to the porous medium equation that lives in any $L^p$ space. So you cannot prove any estimates of the form you wrote with $f(t)$ decaying, at least without further assumptions on the allowed data.
2d
comment numerical method (implicit) for nonlinear pde
At the present it is not clear to me which parts of your question is the motivation and which part is related to the actual question you want to ask. For example, do you not already have a representation formula for which you can set $F = 1$? Then whey are you solving a PDE? And in the representation formula what are $\lambda_u$ and $\lambda_s$? Are they important? Please edit your question to clearly delineate what your question is actually.
2d
comment numerical method (implicit) for nonlinear pde
Are you solving the initial value problem with data on $t = 0$ and going forward in time? If so, the fact that you have positive coefficients $\sigma^2(\lambda - \underline{\lambda})^2 A_{\lambda\lambda}$ should give you instability in the equation (since it looks like a backward heat equation). Or are you solving it for $t < 0$?
2d
comment Results true in a dimension and false for higher dimensions
@ChristianRemling: I hope you don't mind me editing in the gist of the proofs into your answer.
2d
revised Results true in a dimension and false for higher dimensions
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