From inside Tibet it's very difficult to know, because essentially Tibet has been shut down for foreign journalists, foreign tourists, and even Chinese tourism is discouraged. Having said that, you do get some hints and some information, where they say they understand the stance of the Tibet administration, that we discourage self-immolation. They also know it brings tears and sadness to His Holiness the Dalai Lama to have Tibetans self-immolate. They understand all that, but they say, what else can we do? They insist that with 107 self-immolators so far, not even a single Chinese person has been harmed; not even a single Chinese restaurant, hotel, or anything Chinese has been harmed or hurt. That's what they say: We are Buddhists; we cannot harm anybody, but the last resort we are left with is harming ourselves.
If you read the article in The New York Times, it says Tibetans travel from village to village in groups on their motorbikes, wherever the self-immolations are taking place, and they pray; they join the prayers. In that sense, the people seem to pray for the self-immolators and those who have died. It is generally known in Tibet about self-immolators, and the support, from a humanitarian point of view, is extended to the family members who are left behind.