Electron. J. Differential Equations, Vol. 2016 (2016), No. 323, pp. 1-24.

Partial continuity for a class of elliptic systems with non-standard growth

Jihoon Ok

We study partial Holder continuity of weak solutions to elliptic systems with variable non-standard growth, which are related to the function $\Phi(x,t):=t^{p(x)}\log(e+t)$. We prove that weak solutions are Holder continuous for any Holder exponent, except Lebesgue measure zero sets, if systems satisfy certain continuity assumptions. In particular, the variable exponent functions p(.) are assumed to satisfy so-called vanishing log-Holder continuity.

Submitted October 24, 2016. Published December 20, 2016.
Math Subject Classifications: 35B65, 35J60.
Key Words: Partial continuity; elliptic system; non-standard growth; variable exponent.

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Jihoon Ok
School of Mathematics
Korea Institute for Advanced Study
Seoul 02455, Korea
email: jihoonok@kias.re.kr

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