This should work:
string domain = "defaultDomain";
string[] splittedAuth = Request.ServerVariables["LOGON_USER"].Split('\\');
domain = (splittedAuth.Count() > 1) ? splittedAuth[0] : domain;
PrincipalContext context = new PrincipalContext(ContextType.Domain, domain);
If you were referring to the Environment.UserDomainName Property, this is definitely not what you need, as it will return the domain of the account under which the code is executed, which is not the scenario for ASP.NET.