A study of second order semilinear elliptic PDE involving measures

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...

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Bibliographic Details
Published in:arXiv.org 2018-08
Main Authors: Ratan Kr Giri, Choudhuri, Debajyoti
Format: Article
Language:English
Subjects:
Boundary value problems
Partial differential equations
Radon
Online Access:Get full text
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Summary: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.
ISSN:2331-8422