Unfortunately, this does not work.
My code is:
function onHeaderMouseDown () {
}
$el.dialog('header').find('.panel-title').on('mousedown', onHeaderMouseDown);
In the debugger, permanent errors:
Uncaught TypeError: Cannot read property 'target' of undefined
    at _43 (jquery.easyui-1.5.1.min.js:444)
    at jquery.easyui-1.5.1.min.js:638
And 
Uncaught TypeError: Cannot read property 'show' of undefined
    at _295 (jquery.easyui-1.5.1.min.js:3701)
    at HTMLDivElement.onDrag (jquery.easyui-1.5.1.min.js:3664)
    at HTMLDocument._49 (jquery.easyui-1.5.1.min.js:484)
    at HTMLDocument.dispatch (jquery.min.js:3)
    at HTMLDocument.q.handle (jquery.min.js:3)
Without a handler, everything works correctly.
I use jQuery EasyUI 1.5.1, jQuery v3.1.0.