Weighted variable exponent Sobolev estimates for elliptic equations with non-standard growth and measure data

The Anh Bui*, Xuan Thinh Duong

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    Consider the following nonlinear elliptic equation of p(x)-Laplacian type with nonstandard growth {diva(Du,x)=μ in Ω, u=0 on ∂Ω, where Ω is a Reifenberg domain in Rn, μ is a Radon measure defined on Ω with finite total mass and the nonlinearity a: Rn× Rn→ Rn is modeled upon the p(·) -Laplacian. We prove the estimates on weighted variable exponent Lebesgue spaces for gradients of solutions to this equation in terms of Muckenhoupt–Wheeden type estimates. As a consequence, we obtain some new results such as the weighted Lq- Lr regularity (with constants q < r) and estimates on Morrey spaces for gradients of the solutions to this non-linear equation.

    Original languageEnglish
    Article number28
    Pages (from-to)1-37
    Number of pages37
    JournalNonlinear Differential Equations and Applications
    Volume25
    Issue number4
    DOIs
    Publication statusPublished - 1 Aug 2018

    Keywords

    • Measure data
    • Nonlinear p(x)-Laplacian type equation
    • Reifenberg domain
    • Weighted generalized Lebesgue spaces

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