Norm sensitivity of sparsity regularization with respect to p

We consider the Tikhonov functional incorporating a ℓp-norm as a penalty term. The minimizer of this functional is investigated in regard to its sensitivity with respect to the parameter p. To quantify the sensitivity of the minimizer, we determine the derivative with respect to p. The underlying idea is based on the implicit function theorem. We show that the minimizer of the Tikhonov functional is differentiable with respect to p for any 1 < p < 2. For p = 1, the derivative exists only under additional assumptions. (paper)