OAI/Analysis/BernoulliCone/MinimizerStationarity.lean
2 declarations, 0 contain sorry, 0 declared as axioms
- lemma
OAI.Bernoulli.GlobalMinimizer.nonneg_of_continuousline 13 - theorem
OAI.Bernoulli.GlobalMinimizer.stationarityline 26Source documentation
Compact rank-one domain variations give the Bernoulli stress identity from unrestricted Sobolev minimality, including the volume term.
theorem GlobalMinimizer.stationarity {u : Space d → ℝ} {L : ℝ≥0} (hm : GlobalMinimizer u) (huLip : LipschitzWith L u) {a : Space d} {R : ℝ} (hR : 0 < R) {φ : Space d → ℝ} (hφ : Test (ball a R) φ) (e : Space d) : (∫ x in ball a R, Shape.stressTerm u φ e x) = 0 := by …Mentions: OAI.Bernoulli.Space, OAI.Bernoulli.GlobalMinimizer, OAI.Bernoulli.Test, OAI.Bernoulli.Shape.stressTerm