# A proof of Calabi's conjecture using Sobolev space theory

• @Spenser In my understanding, the part using the Sobolev norms is for the $C^0$-estimate. In this part, the Sobolev inequality is used, so in some sense, I agree that Sobolev space theory is used in the proof. However, my intention for the question is more like about some use of weak solutions: to show existence of some weak solution, and to guarantee it is a strong solution by some regularity results. – Yongmin Park Mar 1 at 7:13