Furthermore, the cogging torque of an interior permanent magnet in-wheel motor with 12 slots and 10 poles was investigated using finite element method under three conditions of ideal condition, elliptical stator existed and magnet offset respectively.

The theory of dealing with elliptic operator is given and proved,which divides the inner product of the operator into two operators that are estimated one by one.

Discusses the relation between the dimension of the space R N and the first Dirichlet eigenvalue of second order linear elliptic operator by prababilistic method.

Based on elliptic operators,the initial boundary value problem:u/t-λ(/t)(2u/x2)+(4Φ(u))/x4=0,(x,t)∈QT,u(0,t)=u(1,t)=ux(0,t)=ux(1,t)=0,t∈(0,T),u(x,0)=u0(x),x∈(0,1),λ≥0,QT=(0,1)×(o,T),Φ(u)=|u|q-2u,q>1,has at most one L2 solution.

In this paper,the eigenvalue problem about uniformly elliptic operators of the four orders with weighted functions is studied.