  We propose quite a new method of analyzing the dynamical chiral symmetry
breaking in gauge theories. Starting with the non-perturbative renormalization
group equation for the Wilsonian fermion potential, we define the weak solution
of it in order to mathematically authorize solutions with singularity. The weak
solution is obtained uniquely and it successfully predicts the physically
correct vacuum, chiral condensates, dynamical mass, through its
auto-convexizing power for the effective potential. Thus it works perfectly
even for the first order phase transition in the finite density QCD.
