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arXiv · 1605.00870

A study of second order semilinear elliptic PDE involving measures

Ratan Kr Giri·Debajyoti Choudhuri
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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.

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Ratan Kr Giri, Debajyoti Choudhuri. 2016-04-30. A study of second order semilinear elliptic PDE involving measures. https://arxiv.org/abs/1605.00870

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