PDE

Results named in Tau Ceti's TauCeti.Analysis.PDE modules and in no roadmap's section, as Tau Ceti has them at commit ace60277.

The Caccioppoli inequality to The local Harnack inequality

• The Caccioppoli inequality
• Cauchy--Schwarz for jet fields
• The centered Harnack inequality on a planar disk
• Duhamel's formula for the heat equation
• Duhamel's identity in supremum norm
• Duhamel's principle in integrated form
• The Fredholm alternative in eigenvalue language
• The global Schauder estimate on the whole space
• Green's first identity against H¹₀(Ω)
• Gårding's inequality on H¹(Ω)
• Harnack's convergence theorem
• Harnack's inequality
• The Hopf–Lax subsolution inequality
• Hölder bound on the Laplacian of a heat convolution
• Hölder bounds on the derivatives of a heat convolution
• The Hölder estimate for the Hessian of the Duhamel potential
• The interior Calderón–Zygmund estimate for continuous coefficients
• The interior Schauder estimate on small balls
• The limit in Harnack's convergence theorem is harmonic
• The local Harnack inequality

The localized Calderón–Zygmund… to The zero-forcing Caccioppoli…

• The localized Calderón–Zygmund estimate for coefficients of small oscillation
• Moser's lower bound from small negative powers
• The parabolic Hölder estimate of the Cauchy heat potential
• Perron's theorem
• Pointwise Gårding inequality
• The Rayleigh principle for the Dirichlet problem
• Schauder estimate for a Hessian supported in a ball
• The sharp Poincaré inequality on an interval
• The spatial Hölder estimate of the Cauchy heat potential
• The spectral theorem for the Dirichlet problem
• Stampacchia's global bound
• The temporal Hölder estimate of the Cauchy heat potential
• The value-field parabolic Hölder estimate for the Duhamel potential
• The Weitzenböck formula at a vortex
• The zero-forcing Caccioppoli inequality for a positive truncation of a weak subsolution

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