On the study of some non-coercive elliptic equations in anisotropic weighted Sobolev spaces
Year: 2024
Type: article
Abstract: The primary focus of this paper is to establish some properties and lemmas concerning weighted anisotropic Sobolev spaces. As an application, we consider the following strongly nonlinear and non-coercive elliptic equation $$\label{p1} \left\{\begin{array}{lll} \displaystyle - \sum_{i=1}^{N}D^{i} a_{i}(x,u,\nabla u) + g(x,u,\nabla u) = f(x,u) & \mbox{ in } \Omega, \\ \displaystyle u = 0 & \mbox{ on } \partial \Omega, \end{array}\right.$$ where the right-hand side $f(x,s)$ verifying only a growth condition in $L^{1}(\Omega).$ We study the existence and regularity of renormalized solutions for our elliptic equation in the anisotropic weighted Sobolev spaces.\\ \textbf{ Mathematics Subject Classification (2020).} 46E35, 35J20, 35J60.\\ \textbf{Key words and phrases :} Anisotropic weighted Sobolev spaces, degenerate coercivity, non-coercive elliptic problems, renormalized solution.
Source: PRSM
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W6965301415
FWCI:
Cites:
Cited by:
Related to: