CALDERÓN-ZYGMUND TYPE ESTIMATES FOR A CLASS OF OBSTACLE PROBLEMS WITH p(x) GROWTH
نویسندگان
چکیده
For minimizers u ∈W 1,p(x)(Ω) of quasiconvex integral functionals of the type F [u] := ∫ Ω f(x,Du(x)) dx with p(x) growth in the class K := {u ∈ W 1,p(x)(Ω) : u ≥ ψ}, where ψ ∈ W 1,p(x)(Ω) is a given obstacle function, we show estimates of Calderón-Zygmund type, i.e. |Dψ|p(·) ∈ L =⇒ |Du|p(·) ∈ L , for any q > 1, provided that the modulus of continuity ω of the exponent function p satisfies the condition ω(ρ) log 1 ρ → 0 as ρ→ 0.
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