English

A study of second order semilinear elliptic PDE involving measures

Analysis of PDEs 2018-08-22 v4

Abstract

The objective of this article is to study the boundary value problem for the general semilinear elliptic equation of second order involving L1L^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 L1L^1 function. However, a `{\it very weak}' solution need not exist when an L1L^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.

Keywords

Cite

@article{arxiv.1605.00870,
  title  = {A study of second order semilinear elliptic PDE involving measures},
  author = {Ratan Kr Giri and Debajyoti Choudhuri},
  journal= {arXiv preprint arXiv:1605.00870},
  year   = {2018}
}