I don't think that there's an issue with oral bioavailability of L carnitine, but is used via subcutaneous injections or i think (without being 100% sure) intramuscular injections in order to "target" specific areas of "stubborn" fat. But i dont think that there are any studies on it, only anecdotal evidence from bbing forums and such...
The only use od injectable l carnitine that ive heard until now is IV injections on race horses and dogs to improve performance...