In Apache version 1.2, the error log message about dumped core includes the directory where the dump file should be located. However, many Unixes do not allow a process that has called
setuid() to dump core for security reasons; the typical Apache setup has the server started as root to bind to port 80, after which it changes UIDs to a non-privileged user to serve requests.
Dealing with this is extremely operating system-specific, and may require rebuilding your system kernel. Consult your operating system documentation or vendor for more information about whether your system does this and how to bypass it. If there is a documented way of bypassing it, it is recommended that you bypass it only for the httpd server process if possible.
The canonical location for Apache's core-dump files is the ServerRoot directory. As of Apache version 1.3, the location can be set via the CoreDumpDirectory directive to a different directory. Make sure that this directory is writable by the user the server runs as (as opposed to the user the server is started as).