Continuity of cutoff error coefficients

The scalar coefficients in the short-time heat error are continuous and therefore bounded on each compact cutoff support.

noncomputable def ESS.buShortCutoffHeatScalarSize (scale R : ℝ) (hR : 0 < R) (ε : ℝ) (z : CKN.Foundation.Parabolic.ParabolicPoint) : ℝ

The absolute scalar heat derivative of the smooth cutoff.

Equations

• One or more equations did not get rendered due to their size.

theorem ESS.buShortCutoffGradientSize_continuous (scale R : ℝ) (hR : 0 < R) (ε : ℝ) : Continuous (buShortCutoffGradientSize scale R hR ε)

The spatial derivative size of the smooth cutoff is continuous.

theorem ESS.buShortCutoffHeatScalarSize_continuous (scale R : ℝ) (hR : 0 < R) (ε : ℝ) : Continuous (buShortCutoffHeatScalarSize scale R hR ε)

The absolute heat derivative of the smooth cutoff is continuous.