# A study of second order semilinear elliptic PDE involving measures

Ratan Kr Giri*, Debajyoti Choudhuri

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

## Abstract

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.
Original language English 2489-2506 18 Filomat 33 8 https://doi.org/10.2298/FIL1908489G Published - 2019 A1 Journal article-refereed

## Keywords

• Elliptic PDE
• Reduced limit
• Good measure
• Sobolev space
• EQUATIONS