Local bounds, Harnack inequality and Hölder continuity for divergence type elliptic equations with nonstardard growth

2013/09/09 by Noemí Wolanski, wolanski, Noemi
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1309.2227

openalex publication_date 2013/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we obtain a Harnack type inequality for solutions to elliptic equations in divergence form with non-standard p(x)-type growth. A model equation is the inhomogeneous p(x)-laplacian. Namely, Δ_p(x)u:=div(|∇ u|^p(x)-2∇ u)=f(x)\quadin Ω for which we prove Harnack inequality when f∈ L^q₀(Ω) if max\1,\frac Np_min\

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