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 -