Partial regularity of minimizers of p(x)-growth functionals with p(x)>1. (June 2017) - Nio, Erika; Usuba, Kunihiro
Abstract: We prove partial regularity of minimizers u for functionals of the following type A ( u ) = ∫ Ω [ ( A i j α β ( x, u ) D α u i D β u j ) p ( x ) / 2 + g ( x, u, D u ) ] d x, assuming that A i j α β ( x, u ) and p ( x ) are sufficiently smooth and that p ( x ) > 1 . We prove that u ∈ C 0, α ( Ω 0 ) for some α ∈ ( 0, 1 ) and an open set Ω 0 ⊂ Ω with H m − γ 1 ( Ω − Ω 0 ) = 0, where H s denotes the s -dimensional Hausdorff measure and γ 1 = inf Ω p ( x ) .