OAI/Geometry/RCD/Sobolev/HarmonicEnergyBound.lean
1 declarations, 0 contain sorry, 0 declared as axioms
Enlarging the bound of a fixed harmonic energy representative
- def
OAI.RegularPointCoordinates.LocalHarmonicEnergy.enlargeBoundline 18Source documentation
The energy function and its full measure equation are unchanged.
def LocalHarmonicEnergy.enlargeBound {U : E →L[ℝ] SobolevSpace μ hQ} {M : PositiveBilinearMeasure X E} {κ : ℝ} {p : X} {r : ℝ} {L H : ℝ≥0} {v : E} (G : LocalHarmonicEnergy μ hQ U M κ p r L v) (hLH : (L : ℝ) ^ 2 ≤ (H : ℝ) ^ 2) : LocalHarmonicEnergy μ hQ U M κ p r H v where …Mentions: OAI.RegularPointCoordinates.SobolevSpace, OAI.RegularPointCoordinates.PositiveBilinearMeasure, OAI.RegularPointCoordinates.LocalHarmonicEnergy