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arXiv · 2111.09603

A comparison principle for the Lane-Emden equation and applications to geometric estimates

Lorenzo Brasco·Francesca Prinari·Anna Chiara Zagati
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Abstract

We prove a comparison principle for positive supersolutions and subsolutions to the Lane-Emden equation for the $p-$Laplacian, with subhomogeneous power in the right-hand side. The proof uses variational tools and the result applies with no regularity assumptions, both on the set and the functions. We then show that such a comparison principle can be applied to prove: uniqueness of solutions; sharp pointwise estimates for positive solutions in convex sets; localization estimates for maximum points and sharp geometric estimates for generalized principal frequencies in convex sets.

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Lorenzo Brasco, Francesca Prinari, Anna Chiara Zagati. 2021-11-18. A comparison principle for the Lane-Emden equation and applications to geometric estimates. https://arxiv.org/abs/2111.09603

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