Research proof index

Jensen's inequality for eLpNorm: the L^p norm of a constant equal to the average is at most the L^p norm of the function. For 1 ≤ p < ⊤, an integrable f, and a finite measure μ: eLpNorm (fun _ => ⨍ x, f x ∂μ) p μ ≤ eLpNorm f p μ This is a consequence of Jensen's inequality for the convex function t ↦ |t|^p, proved here via Hölder's ine...

Sobolev-Poincare for smooth functions on the unit ball.

Sobolev-Poincare inequality on the unit ball.

Sobolev-Poincare inequality for MemW1p in existential form.