Equivalence between radial solutions of different non-homogeneous p-Laplacian type equations

2019/12/19 by Jarkko Siltakoski, Siltakoski, Jarkko
Computer Science · Mathematics · #35D30 #35D40 #35J70 #35J75 #35J92 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #msc:35D30 #msc:35D40 #msc:35J70 #msc:35J75 #msc:35J92

paper · pdf · doi:10.48550/arxiv.1912.08983

arxiv created 2019/12/19 · openalex publication_date 2019/12/19 · arxiv updated 2019/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study radial viscosity solutions to the equation - |Du |^q-2Δ_p^Nu=f( |x |)\quadin B_R⊂ℝ^N, where f∈ C[0,R), p,q∈(1,∞) and N≥2. Our main result is that u(x)=v( |x |) is a bounded viscosity supersolution if and only if v is a bounded weak supersolution to -κΔ_q^dv=f in (0,R), where κ>0 and Δ_q^d is heuristically speaking the radial q-Laplacian in a fictitious dimension d. As a corollary we obtain the uniqueness of radial viscosity solutions. However, the full uniqueness of solutions remains an open problem.

Citations

• C1,α regularity of solutions of some degenerate fully non-linear elliptic equations

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