OAI/Analysis/BernoulliCone/MinimizerStationarity.lean

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2 declarations, 0 contain sorry, 0 declared as axioms

  1. lemma OAI.Bernoulli.GlobalMinimizer.nonneg_of_continuous line 13
  2. theorem OAI.Bernoulli.GlobalMinimizer.stationarity line 26

    Source 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