TY - JOUR

T1 - Generalized Poisson integral and sharp estimates for harmonic and biharmonic functions in the half-space

AU - Kresin, G.

AU - Maz'ya, V.

N1 - Publisher Copyright:
© 2018 EDP Sciences.

PY - 2018

Y1 - 2018

N2 - A representation for the sharp coefficient in a pointwise estimate for the gradient of a generalized Poisson integral of a function f on Rn-1 is obtained under the assumption that f belongs to Lp. It is assumed that the kernel of the integral depends on the parameters α and β. The explicit formulas for the sharp coefficients are found for the cases p = 1, p = 2 and for some values of α, β in the case p = ∞. Conditions ensuring the validity of some analogues of the Khavinson's conjecture for the generalized Poisson integral are obtained. The sharp estimates are applied to harmonic and biharmonic functions in the half-space.

AB - A representation for the sharp coefficient in a pointwise estimate for the gradient of a generalized Poisson integral of a function f on Rn-1 is obtained under the assumption that f belongs to Lp. It is assumed that the kernel of the integral depends on the parameters α and β. The explicit formulas for the sharp coefficients are found for the cases p = 1, p = 2 and for some values of α, β in the case p = ∞. Conditions ensuring the validity of some analogues of the Khavinson's conjecture for the generalized Poisson integral are obtained. The sharp estimates are applied to harmonic and biharmonic functions in the half-space.

KW - Biharmonic functions

KW - Generalized Poisson integral

KW - Harmonic functions

KW - Sharp estimates

KW - Two-parametric kernel

UR - http://www.scopus.com/inward/record.url?scp=85049413139&partnerID=8YFLogxK

U2 - 10.1051/mmnp/2018032

DO - 10.1051/mmnp/2018032

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AN - SCOPUS:85049413139

SN - 0973-5348

VL - 13

JO - Mathematical Modelling of Natural Phenomena

JF - Mathematical Modelling of Natural Phenomena

IS - 4

M1 - 2018032

ER -