The objective of this article is to study the boundary value problem for the general semilinear elliptic equation of second order involving $L^1$ functions or Radon measures with finite total variation. The study investigates the existence and uniqueness of `{ \it very weak}' solutions to the boundary value problem for a given $L^1$ function. However, a `{ \it very weak}' solution need not exist when an $L^1$ function is replaced with a measure due to which the corresponding reduced limits has been found for which the problem admits a solution in a `{ \it very weak}' sense.
Categories: math.AP