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Results tagged with differential-equations
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user 22880
Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
3
votes
0
answers
230
views
A priori estimate for Yamabe solution
We know Schoen's compactness on Yamabe problem:
Let $(M^n,g)$ be a smooth compact Riemannian manifold of dimension
$3\leq n\leq 24$ without boundary. Denote $\Phi$ to be the full set
of arbitrary sol …
- 303
2
votes
1
answer
238
views
A priori estimate of elliptic complex
On a compact Riemannian maniflod $(M,g)$, for an elliptic
complex
$\mathcal{C}_0\overset{L_1}{\longrightarrow}\mathcal{C}_1\overset{L_2}{\longrightarrow}\mathcal{C}_2$ where $L_1$ and $L_2$ are partia …
- 303
1
vote
0
answers
234
views
Optimal Sobolev Inequality
Recall the Optimal Sobolev Inequality:
Let $(M^n,g)$ be a smooth,
compact Riemannian $n (\geq 3)$ manifold with $\hbox{inj}_g\geq i_0,
|Ric(g)|\leq \Lambda g$. Let $\sigma_n=\frac{4(n-1)}{n-2}\frac{1} …
- 303