Traces for Fractional Sobolev Spaces with Variable Exponents
نویسنده
چکیده
In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if p : Ω × Ω → (1,∞) and q : ∂Ω→ (1,∞) are continuous functions such that (n− 1)p(x, x) n− sp(x, x) > q(x) in ∂Ω ∩ {x ∈ Ω: n− sp(x, x) > 0}, then the inequality ‖f‖Lq(·)(∂Ω) ≤ C { ‖f‖Lp̄(·)(Ω) + [f ]s,p(·,·) } holds. Here p̄(x) = p(x, x) and [f ]s,p(·,·) denotes the fractional seminorm with variable exponent, that is given by [f ]s,p(·,·) := inf { λ > 0: ∫
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