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Quantitative regularity à la De Giorgi

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De Giorgi method is a way to prove Hölder regularity of solutions of elliptic and parabolic equations. While in the elliptic case the proof is completely quantitative, in the parabolic case it seems to remain a non quantitative step: the intermediate value lemma. The purpose of this talk is to present a quantitative version of this step after introducing how it is useful to get Hölder regularity.

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