Lifting of fractional Sobolev mappings to noncompact covering spaces
(2025) Annales de l’Institut Henri Poincaré - C - Non Linear Analysis — Vol. 42, n° 1, p. 41-84 (2025)
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- Given compact Riemannian manifolds M and N, a Riemannian covering π:N→N by a noncompact covering space N, 1<p<∞ and 0<s<1, the space of liftings of fractional Sobolev maps in W˙s,p(M,N) is characterized when sp>1 and an optimal nonlinear fractional Sobolev estimate is obtained when moreover sp≥dimM. A nonlinear characterization of the sum of spaces W˙s,p(M,R)+W˙1,sp(M,R) is also provided.
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Van Schaftingen, J. (2025). Lifting of fractional Sobolev mappings to noncompact covering spaces. Annales de l’Institut Henri Poincaré - C - Non Linear Analysis, 42(1), 41-84. https://doi.org/10.4171/aihpc/98 (Original work published 2025)