All papers

All publications, in alphabetical order. Click on the title to get the corresponding pdf file.

Papers and preprints:

1. D. Azagra, Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces, Studia Math. 125 (1997) no. 2, 179–186.

2. D. Azagra, Global and fine approximation of convex functions, Proc. London Math. Soc. 107 (2013) no. 4, 799–824.

3. D. Azagra, Locally C^{1,1} convex extensions of 1-jets, Rev. Mat. Iberoam. 38 (2022), 131-174.

4. D. Azagra, On the global shape of continuous convex functions on Banach spaces, J. Math. Anal. Appl. 486 (no.), 15 June 2020, 123944

5. D. Azagra, A. Cappello, and P. Hajlasz, A geometric approach to second-order differentiability of convex functions., Proc. Amer. Math. Soc. Ser. B 10 (2023), 382-397.

6. D. Azagra and M. Cepedello, Smooth Lipschitz retractions of starlike bodies onto their boundaries in infinite-dimensional Banach spaces, Bull. London Math. Soc. 33 (2001), 443-453.

7. D. Azagra and M. Cepedello, Uniform approximation of continuous mappings by smooth mappings with no critical points on Hilbert manifolds, Duke Math. J. 124 (2004) no. 1, 47-66.

8. D. Azagra and R. Deville, Subdifferential Rolle’s and mean value inequality theorems, Bull. Austral. Math. Soc. 56 (1997), no. 2, 319–329.

9. D. Azagra and R. Deville, James’s theorem fails for starlike bodies in Banach spaces, J. Funct. Anal. 180 (2001), 328-346.

10. D. Azagra, R. Deville and M. Jiménez-Sevilla, On the range of the derivatives of a smooth function between Banach spaces, Math. Proc. Cambridge Philos. Soc. 134 (2003), no. 1, 163–185.

11. D. Azagra and T. Dobrowolski, Smooth negligibility of compact sets in infinite-dimensional Banach spaces, with applications, Math. Annalen 312 (1998), no. 3, 445–463.

12. D. Azagra and T. Dobrowolski, Real-analytic negligibility of points and subspaces in infinite-dimensional Banach spaces, with applications, Canadian Math. Bull. 45 (2002) no.1, 3–11.

13. D. Azagra and T. Dobrowolski, On the topological classification of starlike bodies in Banach spaces, Topology and its Applications 132 (2003), 221-234.

14. D. Azagra, T. Dobrowolski, and M. García-Bravo, Smooth approximations without critical points of continuous mappings between Banach spaces, and diffeomorphic extractions of sets, Advances in Math. Volume 354, 1 October 2019, 106756.

15. D. Azagra, M. Drake, and P. Hajlasz, C^2-Lusin approximation of strongly convex functions, Inventiones Math. 236 (2024), no. 3, 1055-1082.

16. D. Azagra, M. Fabian and M. Jiménez-Sevilla, Exact filling of figures with the derivatives of a smooth function between Banach spaces, Canadian Math. Bull. 48 (2005) no. 4, 481-499.

17. D. Azagra and J. Ferrera, Every closed convex set is the set of minimizers of some $C^{\infty}$ smooth convex function, Proc. Amer. Math. Soc. 130 (2002), no. 12, 3687-3692.

18. D. Azagra and J. Ferrera, Proximal calculus on Riemannian manifolds, Mediterranean J. Math. 2 (2005) no. 4, 437 – 450.

19. D. Azagra and J. Ferrera, Applications of proximal calculus to fixed point theory on Riemannian manifolds, Nonlinear Analysis 67 (2007), 154-174.

20. D. Azagra and J. Ferrera, Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature, Rev. Mat. Complut., 19 (2006), no. 2, 323-345.

21. D. Azagra and J. Ferrera, Regularization by sup-inf convolutions on Riemannian manifolds: an extension of Lasry-Lions theorem to manifolds of bounded curvature, J. Math. Anal. Appl. 423 (2015), 994-1024.

22. D. Azagra, J. Ferrera, M. García-Bravo and J. Gómez-Gil, Subdifferentiable functions satisfy Lusin properties of class $C^1$ or $C^2$, J. Approx. Theory 230 (2018), 1-12.
    

23. D. Azagra, J. Ferrera and J. Gómez-Gil, The Morse-Sard Theorem revisited, Quarterly J. Math. 69 (2018), 887-913.

24. D. Azagra, J. Ferrera and J. Gómez-Gil, Nonsmooth Morse-Sard theorems, Nonlinear Analysis 160 (2017), 53-69.
    

25. D. Azagra, J. Ferrera, J. Gómez-Gil, and Carlos Mudarra, Extensions of convex functions with prescribed subdifferentials, Studia Math. 253 (2020), no.2, 199-213.
    

26. D. Azagra, J. Ferrera and F. López-Mesas, Approximate Rolle’s theorems for the proximal subgradient and the generalized gradient, J. Math. Anal. Appl. 283 (2003), 180-191.

27. D. Azagra, J. Ferrera and F. López-Mesas, Nonsmooth analysis and Hamilton-Jacobi equations on Riemannian manifolds, J. Funct. Anal. 220 (2005) no. 2, 304-361.

28. D. Azagra, J. Ferrera and F. López-Mesas, A maximum principle for evolution Hamilton-Jacobi equations on Riemannian manifolds, J. Math. Anal. Appl. 323 (2006), 473-480.

29. D. Azagra, J. Ferrera, F. López-Mesas and Y. Rangel, Smooth approximation of Lipschitz functions on Riemannian manifolds, J. Math. Anal. Appl. 326 (2007), 1370-1378.

30. D. Azagra, J. Ferrera and B. Sanz, Fixed point and zeros for set-valued mappings on Riemannian manifolds: a subdifferential approach, Set-Valued Anal. 16 (2008), 581-596.

31. D. Azagra, J. Ferrera and B. Sanz, Viscosity solutions to second order partial differential equations on Riemannian manifolds, J. Differential Equations 245 (2008) no. 2, 307-336.

32. D. Azagra, R. Fry, A second order smooth variational principle on Riemannian manifolds, Canad. J. Math. 62 (2010), 242-261.

33. D. Azagra, R. Fry, J. Gómez-Gil, J.A. Jaramillo and M. Lovo, $C^1$-fine approximation of functions on Banach spaces with unconditional basis, Quarterly J. Math. 56 (2005) no. 1, 13-20.

34. D. Azagra, R. Fry and L. Keener, Smooth extensions of functions on separable Banach spaces, Math. Ann. 347 (2010) no. 2, 285-297.

35. D. Azagra, R. Fry and L. Keener, Real analytic approximation of Lipschitz functions on Hilbert space and other Banach spaces, J. Funct. Anal. 262 (2012) no. 1, 124-166.

36. D. Azagra, R. Fry and A. Montesinos, Perturbed smooth Lipschitz extensions of uniformly continuous functions on Banach spaces, Proc. Amer. Math. Soc. 133 (2005) no. 3, 727-734.
    

37. D. Azagra and M. García-Bravo, Some remarks about the Morse-Sard theorem and approximate differentiability, Rev. Mat. Complutense 33 (2020), 161-185.
    

38. D. Azagra, M. García-Bravo, and M. Jiménez-Sevilla Approximate Morse-Sard type results for non-separable Banach spaces. J. Funct. Anal. 287 (2024), no. 4, Paper No. 110488.
    

39. D. Azagra, J. Gómez-Gil and J. A. Jaramillo, Rolle’s theorem and negligibility of points in infinite-dimensional Banach spaces, J. Math. Anal. Appl. 213 (1997), no. 2, 487–495.

40. D. Azagra and P. Hajlasz, Lusin-type properties of convex functions and convex bodies, J. Geom. Anal. 31 (2021), p. 11685-11701.

41. D. Azagra and M. Jiménez-Sevilla, The failure of Rolle’s theorem in infinite-dimensional Banach spaces, J. Funct. Anal. 182 (2001), 207-226.

42. D. Azagra and M. Jiménez-Sevilla, On the size of the sets of gradients of smooth functions and starlike bodies in Hilbert space, Bull. Soc. Math. France 130 (2002), 337-347.

43. D. Azagra and M. Jiménez-Sevilla, Geometrical and topological properties of bumps and starlike bodies in Banach spaces, Extracta Math. 17 no.2 (2002), 151-200.

44. D. Azagra and M. Jiménez-Sevilla, Approximation by smooth functions with no critical points on separable infinite-dimensional Banach spaces, J. Funct. Anal. 242 (2007), 1-36.

45. D. Azagra, M. Jiménez-Sevilla, F. Macià, Generalized motion of level sets by functions of their curvatures on Riemannian manifolds, Calculus of Variations and PDE 33 (2008) no. 2, 133-167.

46. D. Azagra, E. Le Gruyer, C. Mudarra, Explicit formulas for $C^{1,1}$ and $C^{1, \omega}_{\textrm{conv}$ extensions of 1-jets in Hilbert and superreflexive spaces, J. Funct. Anal. 274 (2018), 3003-3032.
    

47. D. Azagra, E. Le Gruyer, C. Mudarra, Kirszbraun’s theorem via an explicit formula, Canadian Math. Bull. 64 (2021), no.1, 142-153.
    

48. D. Azagra. F. Macià, Concentration of symmetric eigenfunctions, Nonlinear Analysis 73 (2010) no.3, 683-688.

49. D. Azagra and A. Montesinos, On diffeomorphisms deleting weak compacta in Banach spaces, Studia Math. 162 (2004), 229-244.

50. D. Azagra and A. Montesinos, Starlike bodies and deleting diffeomorphisms in Banach spaces, Extracta Math. 19 (2004), no. 2, 171–213.

51. D. Azagra and A. Montesinos, Deleting diffeomorphisms with prescribed supports in Banach spaces, preprint, 2003.

52. D. Azagra and C. Mudarra, Global approximation of convex functions by differentiable convex functions on Banach spaces, J. Convex Anal. 22 (2015), 1197-1205.
    

53. D. Azagra and C. Mudarra, Smooth convex extensions of convex functions, Calculus of Variations and PDE (2019) 58: 84. https://doi.org/10.1007/s00526-019-1542-z.

54. D. Azagra and C. Mudarra, Whitney Extension Theorems for convex functions of the classes $C^1$ and $C^{1, \omega}$, Proc. London Math. Soc. 114 (2017), no.1, 133-158.
    

55. D. Azagra and C. Mudarra, An extension theorem for convex functions of class $C^{1,1}$ on Hilbert spaces, J. Math. Anal. Appl. 446 (2017), no. 2, 1167-1182.

56. D. Azagra and C. Mudarra, Global geometry and $C^1$ convex extensions of 1-jets, Analysis and PDE 12 (2019) no. 4, 1065-1099.

57. D. Azagra and C. Mudarra, Prescribing tangent hyperplanes to C1,1 and C1,ω convex hypersurfaces in Hilbert and superreflexive Banach spaces, J. Convex Anal. 27 (2020), no.1, 79-102.

58. D. Azagra and C. Mudarra, Convex C^1 extensions of 1-jets from compact subsets of Hilbert spaces, Comptes Rendus Mathématique 358 (2020) no. 5, 551-556.
    

59. D. Azagra and C. Mudarra, C^{1, omega} extension formulas for 1-jets on Hilbert spaces, Advances in Math., 389 (2021), Paper No. 107928, 44 pp.
    

60. D. Azagra, G.A. Muñoz-Fernández, V.M. Sánchez, J.B. Seoane-Sepúlveda, Riemann integrability and Lebesgue measurability of the composite function, J. Math. Anal. Appl. 354 (2009), 229-233.

61. D. Azagra and D. Stolyarov, Inner and outer smooth approximation of convex hypersurfaces. When is it possible?, Nonlinear Anal. 230 (2023), Paper No. 113225, 20 pp.

62. J. Cubo, D. Azagra, A. Casinos, and J. Castanet, Heterochronic detection through a function for the ontogenetic variation of bone shape, J. Theor. Biology 215 (2002), 57-66.