Open AccessA study of second order semilinear elliptic PDE involving measures
Author(s) -
Ratan Kr. Giri,
Debajyoti Choudhuri
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1908489g
Subject(s) - mathematics , uniqueness , boundary value problem , order (exchange) , elliptic curve , function (biology) , weak solution , mathematical analysis , value (mathematics) , pure mathematics , statistics , finance , evolutionary biology , economics , biology
The objective of this article is to study the boundary value problem for the general semilinear elliptic equation of second order involving L1 functions or Radon measures with finite total variation. The study investigates the existence and uniqueness of ?very weak? solutions to the boundary value problem for a given L1 function. However, a ?very weak? solution need not exist when an L1 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 ?very weak? sense.