A density problem for Sobolev spaces on planar domains

الأصل · EN

We prove that for a bounded simply connected domain Ω⊂ R², the Sobolev space W¹,∞(Ω) is dense in W¹,ᵖ(Ω) for any 1≤ p<∞. Moreover, we show that if Ω is Jordan, then C∞(R²) is dense in W¹,ᵖ(Ω) for 1≤ p<∞.