User menu

Strong approximation of fractional Sobolev maps

Bibliographic reference Bousquet, Pierre ; Ponce, Augusto ; Van Schaftingen, Jean. Strong approximation of fractional Sobolev maps. In: Journal of Fixed Point Theory and Applications, Vol. 15, no.1, p. 133-153 (2014)
Permanent URL
  1. Banyaga Augustin, The Structure of Classical Diffeomorphism Groups, ISBN:9781441947741, 10.1007/978-1-4757-6800-8
  2. Bethuel Fabrice, The approximation problem for Sobolev maps between two manifolds, 10.1007/bf02392449
  3. Bethuel Fabrice, Approximations in trace spaces defined between manifolds, 10.1016/0362-546x(93)e0025-x
  4. Bethuel Fabrice, Zheng Xiaomin, Density of smooth functions between two manifolds in Sobolev spaces, 10.1016/0022-1236(88)90065-1
  5. Bourdaud Gérard, Ondelettes et espaces de Besov, 10.4171/rmi/181
  6. Bourgain Jean, Brezis Haim, Mironescu Petru, H1/2 maps with values into the circle: Minimal Connections, Lifting, and the Ginzburg–Landau equation, 10.1007/s10240-004-0019-5
  7. Bourgain Jean, Brezis Haim, Mironescu Petru, Lifting in Sobolev spaces, 10.1007/bf02791533
  8. Bousquet Pierre, Ponce Augusto C., Van Schaftingen Jean, Density of smooth maps for fractional Sobolev spaces W^{s, p} into \ell simply connected manifolds when s \ge 1, 10.5802/cml.5
  9. P. Bousquet, A. C. Ponce and J. Van Schaftingen, Strong density for higher order Sobolev spaces into compact manifolds. To appear.
  10. Brezis Haïm, Mironescu Petru, Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces : , 10.1007/pl00001378
  11. Brezis H., Nirenberg L., Degree theory and BMO; part I: Compact manifolds without boundaries, 10.1007/bf01671566
  12. Escobedo M.: Some remarks on the density of regular mappings in Sobolev classes of S M -valued functions. Rev. Mat. Univ. Complut. Madrid 1, 127–144 (1988)
  13. Gagliardo E.: Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili. Rend. Semin. Mat. Univ. Padova 27, 284–305 (1957)
  14. Giaquinta Mariano, Mucci Domenico, Density results for the W1/2 energy of maps into a manifold, 10.1007/s00209-005-0820-y
  15. HajŁasz Piotr, Approximation of sobolev mappings, 10.1016/0362-546x(94)90190-2
  16. Hang Fengbo, Lin Fanghua, Topology of sobolev mappings, II, 10.1007/bf02392696
  17. Hardt Robert, Lin Fang-Hua, Mappings minimizing theLp norm of the gradient, 10.1002/cpa.3160400503
  18. Hatcher A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)
  19. M. W. Hirsch, Differential Topology. Grad. Texts in Math. 33, Springer-Verlag, New York, 1994.
  20. Marcus Moshe, Mizel Victor J, Every superposition operator mapping one Sobolev space into another is continuous, 10.1016/0022-1236(79)90113-7
  21. Maz'ya V., Shaposhnikova T., An elementary proof of the Brezis and Mironescu theorem on the composition operator in fractional Sobolev spaces, 10.1007/s00028-002-8082-1
  22. Maz'ya Vladimir, Shaposhnikova Tatyana, On the Brezis and Mironescu conjecture concerning a Gagliardo–Nirenberg inequality for fractional Sobolev norms, 10.1016/s0021-7824(02)01262-x
  23. P. Mironescu, On some properties of S 1 -valued fractional Sobolev spaces. In: Noncompact Problems at the Intersection of Geometry, Analysis, and Topology, Contemp. Math. 350, Amer. Math. Soc., Providence, RI, 2004, 201–207.
  24. P. Mironescu, Sobolev maps on manifolds: Degree, approximation, lifting. In: Perspectives in Nonlinear Partial Differential Equations, Contemp. Math. 446, Amer. Math. Soc., Providence, RI, 2007, 413–436.
  25. Mucci Domenico, Strong density results in trace spaces of maps between manifolds, 10.1007/s00229-008-0234-3
  26. Rivière Tristan, 10.1023/a:1006655723537
  27. Schoen R., Uhlenbeck K.: Boundary regularity and the Dirichlet problem for harmonic maps. J. Differential Geom. 18, 253–268 (1983)
  28. J. W. Vick, Homology Theory: An introduction to Algebraic Topology. 2nd ed., Grad. Texts in Math. 145, Springer-Verlag, New York, 1994.