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NON-HOMOGENEOUS P-LAPLACIAN EQUATIONS ON THE SIERPINSKI GASKET
  • ABHILASH SAHU,
  • M. Guru Prem Prasad
ABHILASH SAHU
Indian Institute of Technology Guwahati
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M. Guru Prem Prasad
Indian Institute of Technology Guwahati
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Abstract

Let $\mathcal{S}$ be the Sierpi\’nski gasket in $\mathbb{R}^2$ and $\mathcal{S}_{0}$ denote the boundary of $\mathcal{S}$. In this paper, we study the following non-homogeneous $p$-Laplacian equation \begin{align*} -\Delta_p u &= \lambda |u|^{q-2} u + f \text{~in}\; \mathcal{S}\setminus\mathcal{S}_0\\ u &= 0\;\mbox{~on}\; \mathcal{S}_0, \end{align*} where $p$, $q$, $\lambda$ are real numbers such that $\lambda >0$, $1

Peer review status:UNDER REVIEW

13 Jun 2021Submitted to Mathematical Methods in the Applied Sciences
16 Jun 2021Assigned to Editor
16 Jun 2021Submission Checks Completed
18 Jun 2021Reviewer(s) Assigned