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Dec
10 |
awarded | Nice Answer |
Jun
25 |
awarded | Yearling |
Apr
26 |
answered | Construction of finite element differential forms based on deRham sequences |
Jan
18 |
answered | reduced symplectic form |
Oct
19 |
awarded | Yearling |
Jul
29 |
answered | Example of symplectic and hamiltonian diffeomorphism on $S^2$ and $T^2$ |
Apr
7 |
answered | integration of a laplacian |
Apr
7 |
comment |
Weakest condition for an integrable, almost-symplectic manifold?
Do you mean Liouville's theorem (the Hamiltonian vector field preserves the symplectic form) or Liouville integrability (maximal set of first integrals in involution)? |
Apr
6 |
comment |
FEM on a Laplacian
$H^{-1}$ is the dual space of $H^1$. This is actually even weaker than being in $ L^2 $ (a.k.a. $H^0$), since it's only a continuous functional when applied to weakly differentiable test functions. For example, consider the 1-D Dirac $\delta$-function, $ \delta = \mathrm{H} ' $, where $\mathrm{H}$ is the Heaviside step function. This is obviously not in $L^2$; however, it is in $H^{-1}$, since $ (\delta, v) = (\mathrm{H}', v) = -(\mathrm{H}, v') \leq \lVert \mathrm{H} \rvert _{L^2} \lVert v \rVert _{H^1} $. This means that you can even make sense of the PDE $ u'' = \delta $. |
Apr
6 |
answered | FEM on a Laplacian |
Dec
23 |
revised |
$\ell^p$ version of singular values
caught a mistake |
Dec
22 |
revised |
$\ell^p$ version of singular values
added 179 characters in body |
Dec
22 |
revised |
Question about Banach's matchbox problem.
added code; edited body |
Dec
22 |
answered | $\ell^p$ version of singular values |
Dec
22 |
answered | Question about Banach's matchbox problem. |
Oct
19 |
awarded | Yearling |
Jun
18 |
answered | Proving Hodge decomposition without using the theory of elliptic operators? |
May
28 |
awarded | Enlightened |
May
28 |
awarded | Nice Answer |
May
26 |
answered | What are “variational crimes” and who coined the term? |