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 languageEnglish
Pages (from-to)2489-2506
Number of pages18
JournalFilomat
Volume33
Issue number8
DOIs
Publication statusPublished - 2019
MoE publication typeA1 Journal article-refereed

Keywords

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

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