English

Elliptic Partial Differential Equation Involving a Singularity and a Radon measure

Analysis of PDEs 2019-07-10 v4

Abstract

The aim of this paper is to prove the existence of solution for a partial differential equation involving a singularity with a general nonnegative, Radon measure μ\mu as its nonhomogenous term which is given as \begin{eqnarray} -\Delta u&=& f(x)h(u)+\mu~\text{in}~\Omega,\nonumber u&=&0~\text{on}~\partial\Omega,\nonumber u&>& 0~\text{on}~\Omega\nonumber, \end{eqnarray} where Ω\Omega is a bounded domain of RN\mathbb{R}^N, ff is a nonnegative function over Ω\Omega.

Keywords

Cite

@article{arxiv.1709.00905,
  title  = {Elliptic Partial Differential Equation Involving a Singularity and a Radon measure},
  author = {A. Panda and S. Ghosh and D. Choudhuri},
  journal= {arXiv preprint arXiv:1709.00905},
  year   = {2019}
}

Comments

21 Pages

R2 v1 2026-06-22T21:32:17.971Z