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# On a degenerate singular elliptic problem

Dr. Prashanta Garain IIT Kanpur
 Speaker Dr. Prashanta Garain IIT Kanpur Jan 18, 2019 from 04:00 PM to 05:00 PM LH 006 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.

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