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to be dented; to be indented; to yield; to give; to sink; to collapse; to cave in
to be beaten; to be overwhelmed; to yield; to give in; to give up
to be disheartened; to feel down; to feel depressed
to suffer a loss; to lose
「凹む」 has another reading with different meanings.
車をぶつけてドアが凹んでしまった。
I hit the car and the door got dented.
試験に落ちて気持ちが凹んでいる。
I failed the exam and I'm feeling down.
缶を踏んで上の部分が凹んでしまう。
I stepped on the can and the top got dented.