2025/08/30 by P Athulya, P, Athulya, Sandeep Verma +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2509.00565
openalex publication_date 2025/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a suitable function A:ℝn→ ℝn, we introduce the A-Laplacian in the Dunkl framework as Δk,A(u) =divk(A(∇ku)), where ∇k is the Dunkl-gradient operator associated with the multiplicity function k and the root system R. We derive the local and global Caccioppoli-type inequality for an element u in the Dunkl-Orlicz-Sobolev space, satisfying the Dunkl-differential inequality -Δk, A(u) ≥ bΦ(u)χ_\ugt;0\. Using the Caccioppoli inequality, we establish a sufficient condition for the nonexistence of a nonzero solution u to the Dunkl-differential inequality.