Optimal estimates for the gradient of harmonic functions in the multidimensional half-space

2009/09/10 by Gershon Kresin, Kresin, Gershon, Vladimir Maz’ya +1
Mathematics · #35B30 (Primary) #35J05 (Secondary) #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.0909.1932

openalex publication_date 2009/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A representation of the sharp constant in a pointwise estimate of the gradient of a harmonic function in a multidimensional half-space is obtained under the assumption that function's boundary values belong to L^p. This representation is concretized for the cases p=1, 2, and ∞.

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