What is the classic paper that derives borrowing constraints from asymmetric information?
I don't know if you refer to the extensive margin (some borrowers not being able to get credit) or to the intensive margin (one borrower not being able to get as much credit as (s)he wants). If you are referring to the former, one of the theoretical papers for borrowing constraints on markets with asymmetric information is the following one:

Stiglitz and Weiss (1981) AER's paper on Credit Rationing in Markets with Imperfect Information.
http://www.jstor.org/stable/1802787?seq=1#page_scan_tab_contents

The argument is very interesting. If lenders cannot distinguish between high risk and low risk borrowers, then the ''market-clearing'' (loosely speaking) equilibrium interest rates will be such that identical (to the observer) consumers can be rationed out.

Other good papers are Bester's (1985) AER's paper on Screening vs. Rationing in Credit Markets with Imperfect Information. http://www.jstor.org/stable/1821362?seq=1#page_scan_tab_contents

Finally Chapter 16 on the Handbook of Monetary Economics by Jaffee and Stiglitz may help you.