Mappings of finite distortion: Formation of exponential cusp

الأصل · EN

We consider a quasi-convex planar domain Ωwith a rectifiable boundary containing an exponential cusp and show that there is no homeomorphism f: ²→² of finite distortion with (λK)∈ Lloc¹(²) for some λ>0 such that f(B)=Ω. On the other hand, if we only require that Kf(x)∈ Llocᵖ(²), then such an f exists.