I was going to suggest the \unicode macro as well. One caveat is that this relies on the fonts available on the user's computer, since these characters aren't in the MathJax web-based fonts, so you can't guarantee that they will be displayed properly.
An alternative would be do define \llbracket as [\!\![ and \rrbracket as ]\!\!], which are the "poor man's" versions of these characters. Of course, they are not stretchy, so can't be used with \left and \right.
As Fred mentioned, the next release of MathJax does include more stretchy characters, and U+27E6 and U+27E7 are included in that list when the STIX fonts are available on the user's computer. But the MathJax web fonts dont' include the required characters to make these stretchy characters, so it would require the user to have the STIX fonts installed. If you want to have this right now, you can use your own configuration file to add these stretchy characters, as follows:
<script type="text/x-mathjax-config">
MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () {
var TEXDEFS = MathJax.InputJax.TeX.Definitions;
TEXDEFS.delimiter["\\llbracket"] = "27E6";
TEXDEFS.delimiter["\\rrbracket"] = "27E7";
});
MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function () {
var HTMLCSS = MathJax.OutputJax["HTML-CSS"],
DELIMITERS = HTMLCSS.FONTDATA.DELIMITERS;
var GENERAL = "STIXGeneral",
SIZE1 = "STIXSizeOneSym",
SIZE2 = "STIXSizeTwoSym",
SIZE3 = "STIXSizeThreeSym",
SIZE4 = "STIXSizeFourSym";
if (HTMLCSS.fontInUse === "STIX") {
// left white square bracket
DELIMITERS[0x27E6] = {
dir: "V", HW: [[.93,GENERAL],[1.23,SIZE1],[1.845,SIZE2],[2.46,SIZE3],[3.075,SIZE4]],
stretch: {top:[0x2553,GENERAL], ext:[0x2551,GENERAL], bot:[0x2559,GENERAL]}
};
// right white square bracket
DELIMITERS[0x27E7] = {
dir: "V", HW: [[.93,GENERAL],[1.23,SIZE1],[1.845,SIZE2],[2.46,SIZE3],[3.075,SIZE4]],
stretch: {top:[0x2556,GENERAL], ext:[0x2551,GENERAL], bot:[0x255C,GENERAL]}
};
}
});
</script>
This will define the data needed for the stretchy delimiters, and defined \llbracket and \rrbracket as those delimiters.
Since the characters are only available in the STIX fonts, not the MathJax web-based fonts, you would probably want to change the preferred font to be STIX rather than the MathJax TeX fonts (though if neither is available locally, the web-based MathJax fonts will still be used):
You can, of course, make a local configuration file that includes both of these.
Hope that helps.