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Results tagged with differential-equations
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user 121820
Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
2
votes
Kelvin transformation in fully nonlinear equation
This follows easily from the fact that the Kelvin transform is a conformal diffeomorphism and the naturality of the Schouten tensor.
Let $\Phi(z) := \frac{z}{\lvert z\rvert^2}$ denote the Kelvin trans …
- 1,713
3
votes
The linearization problem of fully nonlinear equation on standard sphere
Here is my favorite way to do this computation.
Let
$$ \delta_{i_1 \dotsm i_k}^{j_1 \dotsm j_k} = \begin{cases} \mathrm{sgn}\, \sigma, & \text{if $j_k = i_{\sigma(k)}$}, \\ 0, & \text{otherwise} \end{ …
- 1,713
7
votes
Nirenberg problem in conformal change
Yes, it is true. This is a consequence of the conformal invariance of the conformal Laplacian.
Let $(M^n,g)$ be a Riemannian manifold. The conformal Laplacian is
$$ L_2^g = -\Delta + \frac{n-2}{4(n- …
- 1,713