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.

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

Brasco L.
Co-primo
;
Prinari F.
Co-primo
;
2022

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.
2022
Brasco, L.; Prinari, F.; Zagati, A. C.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2488946
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