Opuscula Math. 40, no. 4 (2020), 483-494
https://doi.org/10.7494/OpMath.2020.40.4.483
Opuscula Mathematica
Properties of solutions to some weighted p-Laplacian equation
Abstract. In this paper, we prove some qualitative properties for the positive solutions to some degenerate elliptic equation given by \[-\text{div}\big(w|\nabla u|^{p-2}\nabla u\big)=f(x,u),\quad w\in \mathcal{A}_p,\] on smooth domain and for varying nonlinearity \(f\).
Keywords: \(p\)-Laplacian, degenerate elliptic equations, weighted Sobolev space.
Mathematics Subject Classification: 35A01, 35J62, 35J70.
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- Prashanta Garain
https://orcid.org/0000-0001-6285-9329- Aalto University, Department of Mathematics and System Analysis, Espoo-02150, Finland
- Communicated by Patrizia Pucci.
- Received: 2019-06-03.
- Revised: 2020-03-20.
- Accepted: 2020-05-18.
- Published online: 2020-07-09.
