Quantitative parabolic regularity à la De Giorgi

Guerand, Jessica

Séminaire Laurent Schwartz — EDP et applications (2018-2019), Exposé no. 6, 21 p.

We deal with the De Giorgi Hölder regularity theory for parabolic equations with rough coefficients. We give a quantitative proof of the interior Hölder regularity of solutions of parabolic equations using De Giorgi method. More precisely, we give a quantitative proof of the last non quantitative step of the method for parabolic equations, namely the intermediate value lemma, one of the two main tools of the De Giorgi method sometimes called “second lemma of De Giorgi”.

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