Diffeomorphic approximation of planar Sobolev homeomorphisms in rearrangement invariant spaces
Daniel Campbell, Luigi Greco, Roberta Schiattarella, Filip Soudský · ESAIM Control Optimisation and Calculus of Variations · 2021
Let Ω ⊆ ℝ2 be a domain, let X be a rearrangement invariant space and let f ∈ W1 X (Ω, ℝ2) be a homeomorphism between Ω and f(Ω). Then there exists a sequence of diffeomorphisms fk converging to f in the space W1X (Ω, ℝ2).