Degenerated and Competing Horizontal (p, q)-Laplacians with Weights on the Heisenberg Group. (17th February 2023)

• Record Type: Journal Article
• Authors: Razani, A.; Figueiredo, Giovany M.
• Is Part Of: Numerical functional analysis and optimization. Volume 44:Number 3(2023)
• Page Start: 179
• Page End: 201
• Publication Date: 2023-02-17
• Subjects: Competing (p -- q)-Laplacian -- convection -- degenerated (p -- q)-Laplacian -- finite dimensional approximation -- generalized solution -- Heisenberg group -- weak solution -- weighted Sobolev space; 35J92 -- 35B65 -- 35J70 -- 46E35 -- 47H30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2163503
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, the degenerated horizontal ( p, q )-Laplacian with weights − Δ H, p a ( u ) − Δ H, q b ( u ) = f ( ξ, u, D H u ) and the competing horizontal ( p, q )-Laplacian with weights − Δ H, p a ( u ) + Δ H, q b ( u ) = f ( ξ, u, D H u ) including the Dirchlet boundary condition are studied. The existence and approximation results for these problems are studied where 1 < q < p < ∞, f : Ω × R × H n → R is a Carathéodory function, Ω is a bounded smooth domain in the Heisenberg group H n and Δ H, p stands for the horizontal p -Laplacian on H n . The proofs are based on weighted Heisenberg Sobolev spaces, Nemytskij operators, Browder-Minty Theorem, and finite dimensional approximation.