Uniform boundedness principles for Sobolev maps into manifolds
(2019) Annales de l’Institut Henri Poincaré - C - Non Linear Analysis — Vol. 36, n° 2, p. 417-449 (2019)
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- Abstract
- Given a connected Riemannian manifold N, an m-dimensional Riemannian manifold M which is either compact or the Euclidean space, p∈[1,+∞) and s∈(0,1], we establish, for the problems of surjectivity of the trace, of weak-bounded approximation, of lifting and of superposition, that qualitative properties satisfied by every map in a nonlinear Sobolev space Ws,p(M,N) imply corresponding uniform quantitative bounds. This result is a nonlinear counterpart of the classical Banach–Steinhaus uniform boundedness principle in linear Banach spaces.
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Monteil, A., & Van Schaftingen, J. (2019). Uniform boundedness principles for Sobolev maps into manifolds. Annales de l’Institut Henri Poincaré - C - Non Linear Analysis, 36(2), 417-449. https://doi.org/10.1016/j.anihpc.2018.06.002 (Original work published 2019)