Mollification
= Mollification
{title2=$u_\delta=u*\rho_\delta$}
Mollification is the regularization of a <function> or <distribution> by <convolution> with a rescaled <mollifier>. It creates <smooth functions> on interior regions, preserves constant-coefficient distributional equations there, and converges back to the original object in the appropriate local topology as the radius tends to zero. The process is distinct from the kernel used to perform it.