I see many papers on ResearchGate that are recent downloaded papers from Elsevier's website and not an author's copy. Is there a mechanism to report such copyright issues to Elsevier?
You don't report such copyright infringement to Elseveir, but to ResearchGate. https://www.researchgate.net/application.IntellectualPropertyPolicy.html reads:
It is our policy to respond to notices of claimed copyright infringement submitted by rights owners in accordance with the notice and takedown procedures found in section 512(c) of the Digital Millennium Copyright Act (United States) and the European eCommerce Directive, detailed below. Our Designated Agent for receiving notices of claimed copyright and other intellectual property infringement is:
Berlin, Germany, 10115
Telephone: +49 (0) 30 200051-100
I have three notes:
Since you are not the copyright holder, this contact may not be the best one. I doubt that there is a contact to report violation of content that is not yours: Elseveir already have an army of bots and lawyers to do that for them.
Before making such a report, you should be absolutely sure that there indeed was a copyright infringement. For that, you should read https://www.elsevier.com/about/our-business/policies/copyright/permissions or consult http://www.sherpa.ac.uk/romeo/index.php But, as Nate Eldredge noted, without being the copyright holder, you can't be absolutely sure that there was a copyright infringement.
The morality or usefulness of such a report is a completely different question, but I believe a large part of the researchers will tell you: don't do that.