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Flat Level Set Regularity of $p$-Laplace Phase Transitions, PDF eBook

Flat Level Set Regularity of $p$-Laplace Phase Transitions PDF

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We prove a Harnack inequality for level sets of $p$-Laplace phase transition minimizers.

In particular, if a level set is included in a flat cylinder, then, in the interior, it is included in a flatter one.

The extension of a result conjectured by De Giorgi and recently proven by the third author for $p=2$ follows.

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