Regularity results for a class of obstacle problems under nonstandard growth conditions

Abstract

We prove regularity results for minimizers of functionals F ( u , Ω ) : = ∫ Ω f ( x , u , D u ) d x in the class K : = { u ∈ W 1 , p ( x ) ( Ω , R ) : u ⩾ ψ } , where ψ : Ω → R is a fixed function and f is quasiconvex and fulfills a growth condition of the type L −1 | z | p ( x ) ⩽ f ( x , ξ , z ) ⩽ L ( 1 + | z | p ( x ) ) , with growth exponent p : Ω → ( 1 , ∞ ) .