The APM Agent Instrumentination has worked fine for openjdk 1.8.
Started getting the following error after upgrading jvm to openjdk 11.

 4/04/19 12:19:51 PM UTC [ERROR] [IntroscopeAgent.Agent] Invalid tracer registration for plugin "SQL With Params Execute Timer" in extension "Introscope SQL Agent" loaded from "/opt/ca/apm/wily/core/ext/SQLAgent.jar".
4/04/19 12:18:24 PM UTC [ERROR] [IntroscopeAgent.Agent] IntervalHeartbeat.execute threw executing: Waiting for Database Dynamic java.lang.NoClassDefFoundError: java/sql/SQLException
at com.wily.introscope.agent.db.DatabaseManager$3.ITimestampedRunnable_execute(DatabaseManager.java:122)
at com.wily.util.heartbeat.IntervalHeartbeat$BehaviorNode.execute(IntervalHeartbeat.java:972)
at com.wily.util.heartbeat.IntervalHeartbeat.executeNextBehaviorAndCalculateSleepTime(IntervalHeartbeat.java:491)
at com.wily.util.heartbeat.IntervalHeartbeat.access$2(IntervalHeartbeat.java:445)
at com.wily.util.heartbeat.IntervalHeartbeat$HeartbeatRunnable.run(IntervalHeartbeat.java:668)
at java.base/java.lang.Thread.run(Thread.java:834) Caused by: java.lang.ClassNotFoundException: java.sql.SQLException
at com.wily.util.extension.JarExtension$AllPermissionsClassLoader.findClass(JarExtension.java:309) at java.base/java.lang.ClassLoader.loadClass(ClassLoader.java:588)
at com.wily.util.extension.EagerAllPermissionsClassLoader.loadClass(EagerAllPermissionsClassLoader.java:115) at java.base/java.lang.ClassLoader.loadClass(ClassLoader.java:521) 

Is OpenJDK11 supported with the On-premise Java Agent ?

CA APM Java Agent 10.7 
using Docker/Openshift/Kubernetes containers.
Agent configuration is done through Dockerfile and scripts

No, OpenJDK 11 is not supported yet by the standard on-premise Agent yet. 
JDK 8 is tested and works well. Version 9 and above are not supported yet.