Apache Webdav Server user permission for directory access

I configured an apache webdav server as follow:

<VirtualHost *:443>
  Protocols h2 http/1.1
  ServerName webdav.internal.example.local
  SSLEngine on
  SSLCertificateFile /data/certs/cert.pem
  SSLCertificateKeyFile /data/certs/cert.key
  SSLProtocol all -SSLv3
  SSLCipherSuite ECDHE-ECDSA-CHACHA20-POLY1305:ECDHE-RSA-CHACHA20-POLY1305:ECDHE-ECDSA-AES128-GCM-SHA256:ECDHE-RSA-AES128-GCM-SHA256:ECDHE-ECDSA-AES256-GCM-SHA384:ECDHE-RSA-AES256-GCM-SHA384:DHE-RSA-AES128-GCM-SHA256:DHE-RSA-AES256-GCM-SHA384:ECDHE-ECDSA-AES128-SHA256:ECDHE-RSA-AES128-SHA256:ECDHE-ECDSA-AES128-SHA:ECDHE-RSA-AES256-SHA384:ECDHE-RSA-AES128-SHA:ECDHE-ECDSA-AES256-SHA384:ECDHE-ECDSA-AES256-SHA:ECDHE-RSA-AES256-SHA:DHE-RSA-AES128-SHA256:DHE-RSA-AES128-SHA:DHE-RSA-AES256-SHA256:DHE-RSA-AES256-SHA:ECDHE-ECDSA-DES-CBC3-SHA:ECDHE-RSA-DES-CBC3-SHA:EDH-RSA-DES-CBC3-SHA:AES128-GCM-SHA256:AES256-GCM-SHA384:AES128-SHA256:AES256-SHA256:AES128-SHA:AES256-SHA:DES-CBC3-SHA:!DSS
  SSLHonorCipherOrder on
  SSLSessionTickets off

  DavLockDB "/var/lib/dav/DavLock"
  Alias "/shares" "/shares/"
  <Directory "/shares/">
    Dav On
    Options +Indexes
    IndexOptions Charset=UTF-8
    DirectoryIndex disabled
    IndexOptions FancyIndexing
    IndexOptions HTMLTable
    IndexOptions SuppressDescription
    IndexOptions SuppressRules
    IndexOptions NameWidth=*
    IndexOrderDefault Ascending Name
    IndexOptions IgnoreCase
    IndexOptions FoldersFirst
    IndexOptions VersionSort

    AuthType Basic
    AuthName "private area"
    AuthBasicProvider PAM
    AuthPAMService apache
    Require valid-user
  </Directory>

  # These disable redirects on non-GET requests for directories that
  # don't include the trailing slash (for misbehaving clients).
  BrowserMatch "Microsoft Data Access Internet Publishing Provider" redirect-carefully
  BrowserMatch "^Microsoft-WebDAV-MiniRedir" redirect-carefully
  BrowserMatch "MS FrontPage" redirect-carefully
  BrowserMatch "^WebDrive" redirect-carefully
  BrowserMatch "^WebDAVFS/1.[01234]" redirect-carefully
  BrowserMatch "^gnome-vfs/1.0" redirect-carefully
  BrowserMatch "^XML Spy" redirect-carefully
  BrowserMatch "^Dreamweaver-WebDAV-SCM1" redirect-carefully
  BrowserMatch " Konqueror/4" redirect-carefully
  BrowserMatch "^gvfs" redirect-carefully
  BrowserMatch "^Jakarta-Commons-VFS" redirect-carefully

</VirtualHost>

The problem is that the directories are owned by different groups. The apache web server is running with the user www-data and of course this user can't access the directories.

It is possible to configure apache that the user permissions will use the read/write permissions of the authenticated user to access the directory?.

I used also the kerberos authentication, but it hasn't worked.