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Results tagged with ca.classical-analysis-and-odes
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user 58975
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
0
votes
Regular Lagrangian flow for explicit ODE with discontinuous right-hand side
No. The theory of Regular Lagrangian Flows rests on two key assumptions: a Sobolev/BV regularity of the vector field and a bound from below on its divergence.
In your case you are solving
$$
X'=b(X)
$ …
- 660
4
votes
Are there alternative proofs for existence/uniqueness of ODE solutions?
The theory of Di Perna-Lions, also revisited by Ambrosio, provides existence (and uniqueness, in a suitable sense) results for a.e. initial datum of the ODE $\gamma'_t=v_t(\gamma_t)$ under the assumpt …
- 660
3
votes
Gradient flows: convex potential vs. contractive flow?
It should be noticed that already on $R^d$ equipped with a non-Euclidean norm $\|.\|$ the answer to your question is no. Ohta-Sturm [1] proved the following: let $\lambda\in R$ and consider the classe …
- 660