On a degenerate singular elliptic problem
Dr. Prashanta Garain
IIT Kanpur
| Speaker |
Dr. Prashanta Garain
IIT Kanpur
|
|---|---|
| When |
Jan 18, 2019
from 04:00 PM to 05:00 PM |
| Where | LH 006 |
| Add event to calendar |
vCal
iCal
|
Abstract: We provide existence, uniqueness and regularity results of a degenerate singular elliptic boundary value problem whose model is given by
\({-div}\)\((w(x)|\nabla u|^{p-2}\nabla u)\)=\(\frac{f}{u^\delta}\,\,\text{ in }\,\,\Omega,\)
\(u>0\text{ in }\Omega,\\ u = 0 \text{ on } \partial\Omega,\)
where \(\Omega\) is a bounded smooth domain in \(\mathbb{R}^N\) with \(N\geq 2\), \(w\) belong to the Muckenhoupt class \(A_p\) for some \(1<p<\infty\), \(f\) is a nonnegative function belong to some Lebesgue space and \(\delta>0\). The main tools are weighted Sobolev space, embedding theorems and a priori estimates.