Abstract: In[1] we discussed the problems of calculus of variations with strong nonlinearity. Its Euler equation is evidently the following elliptic type equation of divergent form with strongly increasing coefficients,
(da₁(x,u,u_x)/dx_i)+a(a,u,u_x)=0,x∈Ω⊂Rⁿ. (1)
We get the interior regularities of the solutions of(1). It is just the Hilbert's 19th problem in the case with strong nonlinearity.