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.
Keywords: Nonlinear elliptic equation, Measure data, Variable exponent, Calderón–Zygmund type estimate, Reifenberg flat domain
@article{AIHPC_2017__34_7_1639_0, 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 = {http://archive.numdam.org/articles/10.1016/j.anihpc.2016.12.002/} }
TY - JOUR AU - Byun, Sun-Sig AU - Ok, Jihoon AU - Park, Jung-Tae TI - Regularity estimates for quasilinear elliptic equations with variable growth involving measure data JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 1639 EP - 1667 VL - 34 IS - 7 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2016.12.002/ DO - 10.1016/j.anihpc.2016.12.002 LA - en ID - AIHPC_2017__34_7_1639_0 ER -
%0 Journal Article %A Byun, Sun-Sig %A Ok, Jihoon %A Park, Jung-Tae %T Regularity estimates for quasilinear elliptic equations with variable growth involving measure data %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 1639-1667 %V 34 %N 7 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2016.12.002/ %R 10.1016/j.anihpc.2016.12.002 %G en %F AIHPC_2017__34_7_1639_0
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, Volume 34 (2017) no. 7, pp. 1639-1667. doi : 10.1016/j.anihpc.2016.12.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2016.12.002/
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