Theorems · Theorem · ordinary differential equations

IsPicardLindelof.lipschitzOnWith

∀ {E : Type u_1} [inst : NormedAddCommGroup E] {f : ℝ → E → E} {tmin tmax : ℝ} {t₀ : ↑(Set.Icc tmin tmax)} {x₀ : E}
  {a r L K : NNReal},
  IsPicardLindelof f t₀ x₀ a r L K → ∀ t ∈ Set.Icc tmin tmax, LipschitzOnWith K (f t) (Metric.closedBall x₀ ↑a)

The vector field at any time is Lipschitz with constant K within a closed ball.

Defined in: Mathlib.Analysis.ODE.PicardLindelof
Cited by: 5 results in Mathlib
Foundations: Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
Set.Elemstatement and proof · cited by 7,166
NNRealstatement and proof · cited by 4,310
Set.Iccstatement and proof · cited by 1,702
NNReal.toRealstatement · cited by 1,260
Metric.closedBallstatement · cited by 704
LipschitzOnWithstatement · cited by 164
IsPicardLindelofstatement and proof · cited by 33

Cited by5

Results whose statement or proof uses this declaration.

IsPicardLindelof.shrinkproof · cited by 2
IsPicardLindelof.continuousOn_uncurryproof · cited by 2
ODE.FunSpace.dist_comp_iterate_next_leproof · cited by 1
ODE.FunSpace.continuousOn_comp_compProjproof · cited by 1
IsPicardLindelof.weaken_lipschitzproof · cited by 0