In this paper, we focus on the famous Talenti’s symmetrization inequality, more precisely, its Lp corollary which asserts that the Lp-norm of the solution to -Δv=f♯ is higher than the Lp-norm of the solution to -Δu=f (we are considering Dirichlet boundary conditions, and f♯ denotes the Schwarz symmetrization of f:Ω→R+). We focus on the particular case where functions f are defined on the unit ball, and are characteristic functions of a subset of this unit ball. We show in this case that stability occurs for the Lp-Talenti inequality with the sharp exponent 2.
Sharp Quantitative Talenti Inequality in Particular Cases
Acampora P.;
2026-01-01
Abstract
In this paper, we focus on the famous Talenti’s symmetrization inequality, more precisely, its Lp corollary which asserts that the Lp-norm of the solution to -Δv=f♯ is higher than the Lp-norm of the solution to -Δu=f (we are considering Dirichlet boundary conditions, and f♯ denotes the Schwarz symmetrization of f:Ω→R+). We focus on the particular case where functions f are defined on the unit ball, and are characteristic functions of a subset of this unit ball. We show in this case that stability occurs for the Lp-Talenti inequality with the sharp exponent 2.File in questo prodotto:
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