JournalsaihpcVol. 34, No. 7pp. 1639–1667

Regularity estimates for quasilinear elliptic equations with variable growth involving measure data

  • Jihoon Ok

    Korea Institute for Advanced Study, Seoul 02455, Republic of Korea

  • Jung-Tae Park

    Department of Mathematical Sciences, Seoul National University, Seoul 08826, Republic of Korea

  • Sun-Sig Byun

    Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826, Republic of Korea
Regularity estimates for quasilinear elliptic equations with variable growth involving measure data cover
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Abstract

We investigate a quasilinear elliptic equation with variable growth in a bounded nonsmooth domain involving a signed Radon measure. We obtain an optimal global Calderón–Zygmund type estimate for such a measure data problem, by proving that the gradient of a very weak solution to the problem is as globally integrable as the first order maximal function of the associated measure, up to a correct power, under minimal regularity requirements on the nonlinearity, the variable exponent and the boundary of the domain.

Cite this article

Jihoon Ok, Jung-Tae Park, Sun-Sig Byun, Regularity estimates for quasilinear elliptic equations with variable growth involving measure data. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 7, pp. 1639–1667

DOI 10.1016/J.ANIHPC.2016.12.002