/usr/lib/x86_64-linux-gnu/libpetsc_real.so is in libpetsc3.6.2-dev 3.6.2.dfsg1-3ubuntu1.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/x86_64-linux-gnu/libpetsc_real.so.3.6.2
/usr/lib/x86_64-linux-gnu/libpetsc_real.so.3.6.2