The L_q Minkowski problem for p-harmonic measure

2024/12/10 by Hai Li, Li, Hai, Longyu Wu +3
Mathematics · #Mathematical Approximation and Integration #Advanced Harmonic Analysis Research #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2412.07561

Abstract

In this paper, we consider an extremal problem associated with the solution to a boundary value problem. Our main focus is on establishing a variational formula for a functional related to the p-harmonic measure, from which a new measure is derived. This further motivates us to study the Minkowski problem for this new measure. As a main result, we prove the existence of solutions to the L_q Minkowski problem associated with the p-harmonic measure for 0

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