I'm reaally confused that why all the boundary regularity on the p-Laplace type elliptic equation are dealt with the homogeneous Dirichlet boundary conditions, for example, the recent paper of A.Cianchi and V.G.Maz'ya. For the linear equations, there is no problem if we set u=0 on the boundary, but as far as I know it is not equivalent with the nonhomogeneous boundary conditions in the nonlinear case. Can I get some help or instructions?
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