Using the interpolation theory of a family of linear operators and the Sobolevspaces, we introduce a quantity J_∈~4(λ) which depicts the shape of the boundary layer, andthen analyze the boundary singularty of J_∈~4(λ). Our result shows that the thickness of theboundary layer (or the regular region of J_∈~4(λ)) is intrinsically related to the reciprocal ofthe order of the equation; the loss of boundary conditions between the singular solution andthe limit solution does not influence the thickness of the boundary layer, but it influencesthe process of increasing singularity of J_∈~4(λ); the more the loss of boundary conditions, thesmaller the region of increasing singularity. Finally, we give a definition of a neighborhoodof sudden change and propose an open problem regarding this neighborhood.
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