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

Byun, Sun-Sig; Ok, Jihoon; Park, Jung-Tae

doi:10.1016/j.anihpc.2016.12.002

Byun, Sun-Sig ; Ok, Jihoon ; Park, Jung-Tae

Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 7, pp. 1639-1667.

Résumé

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.

MR Zbl

DOI : 10.1016/j.anihpc.2016.12.002

Classification : 35J92, 46F30, 42B37
Mots-clés : Nonlinear elliptic equation, Measure data, Variable exponent, Calderón–Zygmund type estimate, Reifenberg flat domain

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     author = {Byun, Sun-Sig and Ok, Jihoon and Park, Jung-Tae},
     title = {Regularity estimates for quasilinear elliptic equations with variable growth involving measure data},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1639--1667},
     publisher = {Elsevier},
     volume = {34},
     number = {7},
     year = {2017},
     doi = {10.1016/j.anihpc.2016.12.002},
     zbl = {1374.35183},
     mrnumber = {3724751},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2016.12.002/}
}

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Byun, Sun-Sig; Ok, Jihoon; Park, Jung-Tae. Regularity estimates for quasilinear elliptic equations with variable growth involving measure data. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 7, pp. 1639-1667. doi : 10.1016/j.anihpc.2016.12.002. https://www.numdam.org/articles/10.1016/j.anihpc.2016.12.002/

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