/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/ is in libpetsc3.4.2-dev 3.4.2.dfsg1-6.
This file is owned by root:root, with mode 0o755.
..
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petsc.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscao.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscaodef.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscconf.h
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscconfiginfo.h
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscdef.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscdm.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscdmadda.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscdmcomposite.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscdmda.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscdmdadef.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscdmdef.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscdmmesh.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscdmmeshdef.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscfix.h
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscis.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscisdef.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscksp.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petsckspdef.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscmachineinfo.h
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscmat.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscmatdef.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscpc.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscpcdef.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscsnes.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscsnesdef.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscsys.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscsysdef.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscts.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petsctsdef.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscvec.mod
/usr/lib/petscdir/3.4.2/linux-gnu-c-opt/include/petscvecdef.mod