Partial regularity for nonlinear elliptic systems with continuous growth exponent - Habermann, Jens (Annali Di Matematica Pura Ed Applicata, 2013)
For weak solutions of nonlinear elliptic systems of the type -diva(x, u(x), Du(x)) = 0, with nonstandard p(x) growth, we show interior partial Hölder continuity for any Hölder exponent α ∈ (0,1), provided that the exponent function is 'logarithmic Hölder continuous'. The result also covers the up to now open partial regularity for systems with constant growth with exponent p less than two in the case of merely continuous dependence on the spacial variable x. © 2011 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.
UnivIS-Import:2015-03-09:Pub.2013.nat.dma.lma2.partia_4
Keywords: Hölder continuity; Nonlinear elliptic systems; Nonstandard growth; Partial regularity