  In this paper, we address the problem of approximating solutions of ill-posed
problems using mollification. We quickly review existing mollification
regularization methods and provide two new approximate solutions to a general
ill-posed equation $T(f) =g$ where $T$ can be nonlinear. The regularized
solutions we define extend the work of Bonnefond and Mar\'echal \cite{xapi},
and trace their origins in the variational formulation of mollification, which
to the best of our knowledge, was first introduced by Lannes et al.
\cite{lannes}. In addition to consistency results, for the first time, we
provide some convergence rates for a mollification method defined through a
variational formulation.
