Install according to the official document. GitHub - AdoptOpenJDK/homebrew-openjdk: AdoptOpenJDK HomeBrew Tap
$ brew tap AdoptOpenJDK/openjdk
$ brew cask install adoptopenjdk11
$ /usr/libexec/java_home -v 11
/Library/Java/JavaVirtualMachines/adoptopenjdk-11.jdk/Contents/Home
Describe it in .bash_profile or .bashrc as needed.
export JAVA_HOME=/Library/Java/JavaVirtualMachines/adoptopenjdk-11.jdk/Contents/Home
PATH=${JAVA_HOME}/bin:${PATH}
$ java -version
openjdk version "11.0.6" 2020-01-14
OpenJDK Runtime Environment AdoptOpenJDK (build 11.0.6+10)
OpenJDK 64-Bit Server VM AdoptOpenJDK (build 11.0.6+10, mixed mode)
$ javac -version
javac 11.0.6
$ which java
/Library/Java/JavaVirtualMachines/adoptopenjdk-11.jdk/Contents/Home/bin/java
$ which javac
/Library/Java/JavaVirtualMachines/adoptopenjdk-11.jdk/Contents/Home/bin/javac
$ ls /Library/Java/JavaVirtualMachines/adoptopenjdk-11.jdk/Contents/Home/bin/
jaotc		javap		jfr		jmap		jstat		rmiregistry
jar		jcmd		jhsdb		jmod		jstatd		serialver
jarsigner	jconsole	jimage		jps		keytool		unpack200
java		jdb		jinfo		jrunscript	pack200
javac		jdeprscan	jjs		jshell		rmic
javadoc		jdeps		jlink		jstack		rmid
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