Study For Some Problems To P-Harmonic Equation And Quasiregular Mapping

p-Harmonic equation is an important quasilinear elliptic equation, which has sig-nificant applications in quasiconformal analysis and nonlinear elasticity. In this pa-per, we study a weighed p-harmonic equation by using of Hodge decomposition and Young inequality, and obtain the uniqueness for solutions of Dirichlet problem of p-harmonic equation with weight; We also define (K1, K2)-quasiregular mappings of sev-eral n-dimensionalvariables, and obtain a Caccioppoli-type inequality. These results can be regarded as generalizations and developments of the classical ones.