Gefen, still in the middle of the shiva period, asked a rabbi if he could perform on Yom Haatzmaut as originally scheduled. 

Rabbi Dr Yitzchak Ben David paskened that he is allowed to perform as scheduled. Rabbi Ben David said sometimes halacha recognizes the need to go out to work during shiva, especially in a situation of great loss, and especially when great loss will be caused to other people. Still, usually the allowance is for working in private not public in front of others, but some allow that too. Yom Haatzmaut has the status of a day of joy, similar to Chanukah and Purim, and just like on Purim there is no public display of mourning so there is room to say that this is so on Yom Haatzmaut as well.

The Rabbi qualified his allowance by saying that with all that being ok to rely on in this situation, Aviv Gefen himself should not profit from performing during shiva on Yom Haatzmaut but should dedicate the profits in memory of his father and use them to commemorate him. Additionally, during the performance he should explicitly reference the chag, either in song or by reciting psukim of hallel, and he should also reference his late father in a way that will honor his memory.

source: Ynet

the most interesting part of this is that Aviv Gefen asked a shailah