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Results tagged with ap.analysis-of-pdes
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user 47391
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
6
votes
1
answer
432
views
The Yamabe problem and $\phi^4$ scalar field theory?
The other day I happened to be browsing this page on wikipedia: https://en.wikipedia.org/wiki/Mass_gap
In the middle of the page is the equation $$\square\phi+\lambda\phi^3=0$$ where $\square$ is the …
- 787
4
votes
1
answer
143
views
A Certain First-Order Differential Equation for a Closed 2-Form
Suppose we have a Riemannian manifold $(M,g)$ and a fixed vector field $X$. Consider the following equations for a 2-form $F$:
$$dF=0$$ $$(\delta-\iota_X) F=0$$
Here, $\delta$ is the codifferential i …
- 787
3
votes
2
answers
325
views
Converse to Lichnerowicz Vanishing Theorem?
The Lichnerowicz vanishing theorem says that if on a compact 4-dimensional spin manifold there exists a metric whose scalar curvature $R>0$, then there are no harmonic spinors; $$D\psi=0 \implies \psi …
- 787