Selected papers

SELECTED PAPERS (by subject):

Smooth extensions of convex functions:

  1. D. Azagra, Locally C1,1 convex extensions of 1-jets, Rev. Mat. Iberoam. 38, 131-174 (2022).

  2. 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.

  3. 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.

  4. 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.

  5. 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.

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

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), p. 11685-11701.

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

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

  8. 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.

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, Advances in 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, Canadian Math. Bull. 64 (2021), no.1, 142-153.

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, Advances in Math. Volume 354, 1 October 2019, 106756.

  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, 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.

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.