Degenerated and Competing Horizontal (<i>p</i>, <i>q</i>)-Laplacians with Weights on the Heisenberg Group
A. Razani, Giovany M. Figueiredo
Abstract
In this article, the degenerated horizontal (p, q)-Laplacian with weights −ΔH,pa(u)−ΔH,qb(u)=f(ξ,u,DHu) and the competing horizontal (p, q)-Laplacian with weights −ΔH,pa(u)+ΔH,qb(u)=f(ξ,u,DHu) including the Dirchlet boundary condition are studied. The existence and approximation results for these problems are studied where 1<q<p<∞, f:Ω×R×Hn→R is a Carathéodory function, Ω is a bounded smooth domain in the Heisenberg group Hn and ΔH,p stands for the horizontal p-Laplacian on Hn. The proofs are based on weighted Heisenberg Sobolev spaces, Nemytskij operators, Browder-Minty Theorem, and finite dimensional approximation.
Topics & Concepts
Heisenberg groupMathematicsSobolev spaceBounded functionLaplace operatorDomain (mathematical analysis)Group (periodic table)Boundary (topology)p-LaplacianCombinatoricsMathematical analysisPure mathematicsMathematical physicsBoundary value problemPhysicsQuantum mechanicsAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsSpectral Theory in Mathematical Physics