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Results tagged with ap.analysis-of-pdes
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user 38739
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
-2
votes
1
answer
677
views
A Poincare inequality for the Laplace-Beltrami operator [closed]
Suppose $w \in C^2 (S^{n-1}), \Lambda$ is Laplace-Beltrami operator on the sphere $S^{n-1}$, How can I prove follow Poincare inequality :
$\int_{S^{n-1}} w\Lambda w d\sigma \leq (1-n) \int_{S^{n-1}} | …
- 21
2
votes
2
answers
281
views
A general inequality about spherical mean of a function
suppose $\overline u(r)=\frac{1}{\omega_{n-1}}\int_{S^{n-1}}u(r,w)dw,0<r<1,$ is the average of $u(r,w)$ on sphere $S^{n-1}$,where $(r,w)$ are the polar coordinates in $R^n$.
My question is whether ( …
- 21