SELECTED PAPERS (by subject):

Smooth extensions of convex functions:

  1. D. Azagra, Locally C^{1,1} convex extensions of 1-jets, Rev. Mat. Iberoam. 38 (2022) no. 1, 131-174.

  2. 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.

  3. 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.

  4. 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.

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

  6. 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, 81-104.

Extension of functions:

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

  2. D. Azagra and C. Mudarra, $C^{1, \omega}$ extension formulas for 1-jets on Hilbert spaces,  Adv. Math. 389 (2021), paper no. 107928, 44 pp.

  3. 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.

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

Smooth approximation of convex functions:

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

  2. 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.

  3. 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.

  4. D. Azagra and P. Hajlasz, Lusin-type properties of convex functions and convex bodies,  J. Geom. Anal. 31 (2021) no. 12,  11685-11701.

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

  6. D. Azagra and D. Stolyarov, Inner and outer smooth approximation of convex hypersurfaces. When is it possible?, preprint, 2022.


Smooth approximation of functions:
  1. 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.

  2. 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.

  3. 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.

Critical points of differentiable functions on Banach spaces:
  1. D. Azagra, J. Ferrera and J. Gómez-Gil, The Morse-Sard Theorem revisited, Quarterly J. Math. 69 (2018), 887-913.

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

  3. 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.

  4. D. Azagra, T. Dobrowolski, and M. García-Bravo, Smooth approximations without critical points of continuous mappings between Banach spaces, and diffeomorphic extractions of sets, Adv. Math. 354 (2019), 106756, 80 pp.

  5. 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. 

Geometry of Banach spaces:

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

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

  3. 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.

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

  5. 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.

  6. 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.

Viscosity solutions to PDE:
  1. 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.

  2. 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.

  3. 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.