Hello
You have at a minimum of 3 ospf adjacency's from the core by the looks of it, All on multiaccess connections ( probably broadcast network type ) so these would have negotiated DR/BDR adjacency's.
In a multi-access ospf network DR/BDRs are elected so ospf updates/topology info etc is sent centrally from the elected DR of the ospf segment to all other attached ospf rtrs thus negating the need for all the other rtrs sharing the same network segment to do this individually - so manually setting the DR is recommended which then will make the election of the DR/BDR/Drother deterministic..
However If all of these opsf interfaces have just the single OSPF rtr attached them you could negate the DR/BDR election completely and set the each interface to become a P2P network.
It also looks like your ospf rtrs that are adjacent from the core are receiving a default route or at least one is being advertised to them.
I would suggest you to remove this and then check reachability from the lan once more.
For future reference, If the static default routes you are showing on the core are required, maybe append them to be conditional based on the readability of the ISPs connections or some received prefix from either of them, this can be accomplished quite simply with a Boolean and ipsla tracking.
If however you have the option of receiving a default from either ISP instead then you could just cost out the less preferred default if need be so you would have no need to append any static default routes towards either ISP
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Kind Regards
Paul
