knowingly; deliberately; with full knowledge
Used when someone acts while fully aware of a situation, risk, or consequence. Often implies acceptance of the outcome.
Knowing the danger, he went to the rescue.
She decided on the investment fully aware of the risks.
Phrase composed of 承知 (acknowledgment, consent) + の (possessive particle) + 上 (on top of, in addition to) + で (particle indicating state/condition). Literally 'on top of knowing', it means doing something while being fully aware of the circumstances.