How do you write a rewrite-rule that redirects site visitors towards the domain www.mydomain.com/ to www.mydomain.com/index.html?

Would you like to redirect nothing (^$) to index.html? That will take a look like

RewriteRule ^$ index.html [L]

If you wish to avoid both the / and /index.html being listed in search bots, adding R=301 to really make it a permanent redirect as opposed to a temporary redirect (302, the default). This could allow the bots only index the /index.html.

RewriteRule ^$ index.html [R=301,L]

What BalusC stated - but consider whether you want to redirect them. Would not it be easier to just serve index.html once the browser demands /, like the majority of servers do? This is an extra round-visit to the server for no gain and merely helps make the URL longer. It is so the nineteen nineties. :)