(found in 4.3pre17)
Bourne shell "here documents" (<<DELIM ... DELIM) work fine out of the box with jEdit's syntax handling, but the indented version (<<-DELIM ... DELIM) is not recognized for what it is. A simple change to shellscript.xml solves the problem.
<!-- Readins -->
<SPAN_REGEXP HASH_CHAR="<<" TYPE="LITERAL1" DELEGATE="LITERAL">
<BEGIN><![CDATA[<<-?[\p{Space}'"]*([\p{Alnum}_]+)[\p{Space}'"]*]]></BEGIN>
<END AT_LINE_START="TRUE">$1</END>
</SPAN_REGEXP>
The change is altering "<<" in the CDATA to "<<-?".
Another slight error in the above, but I'm not enough of a syntax highlighter expert to figure it out, is that <END AT_LINE_START="TRUE"> is wrong, at least for bash. What *IS* required is that the closing word be the first non-whitespace on the line, and that nothing (including whitespace) follows it. Just setting AT_LINE_START="FALSE" is a quick hack that works kinda-sorta, but that does some bad stuff if you happen to use the closing word somewhere in your text. A better way to do it would be some kind of pattern that says "<line beginning><optional whitespace>$1" but I can't figure out any way to make that work.
Moving to patches tracker.
This is not actually a patch yet. Would you mind making your changes to the current svn trunk of shellscript.xml and generating a patch with "svn patch", attaching it as an attachment to this ticket please?
Also, please attach a sample shellscript file with a here document for testing purposes.