Integral Representation and Estimation of Harmonic Functions in Half-Plane;

The Dirichlet boundary value problem for harmonic function;

Then,we further obtain that each bounded weak solution is of sharp Hlder exponent with anyγ:0≤γ<k under the additional data regularity assumptions,where k is just as the local Hlder index of A-harmonic functions.

karp to prove that on such kind of 2 Mfd which curvature k≥-1r 2 log r outside a compact set there exist no nonconstant subharmonic functions which bounded f.

In this paper, applying Life theory of complex-functional, not only the space harmonic functions in polynomial form but also the spherical functions are obtained.

It is proved for harmonic functions an integral identity.

The basic equations are generalized from those of the transversely isotropic magneto-electro-elastic media, and the general solutions in forms of harmonic functions in the case of distinct eigenvalues are derived.

The basic equations are generalized from those of the transversely isotropic magnetoelectroelastic media, and the general solution in forms of harmonic functions in the case of distinct eigenvalues are derived.