SELECTED PAPERS (by subject):
Smooth extensions of convex functions:
D. Azagra, Locally C^{1,1} convex extensions of 1-jets, Rev. Mat. Iberoam. 38 (2022) no. 1, 131-174.
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.
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.
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.
D. Azagra and C. Mudarra, Global geometry and $C^1$ convex extensions of 1-jets, Analysis and PDE 12 (2019) no. 4, 1065-1099.
D.
Azagra and C. Mudarra, Prescribing
tangent hyperplanes to
J. Convex Anal. 27 (2020) no. 1,
81-104.
Extension of functions:
D. Azagra, R. Fry and L. Keener, Smooth extensions of functions on separable Banach spaces, Math. Ann. 347 (2010) no. 2, 285-297.
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.
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.
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:
D. Azagra, Global and fine approximation of convex functions, Proc. London Math. Soc. 107 (2013) no. 4, 799--824.
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.
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.
D. Azagra and P. Hajlasz, Lusin-type properties of convex functions and convex bodies, J. Geom. Anal. 31 (2021) no. 12, 11685-11701.
D. Azagra and C. Mudarra, Global approximation of convex functions by differentiable convex functions on Banach spaces, J. Convex Anal. 22 (2015), 1197-1205.
D. Azagra and D. Stolyarov, Inner and outer smooth approximation of convex hypersurfaces. When is it possible?, preprint, 2022.
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.
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.
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.
D. Azagra, J.
Ferrera and J. Gómez-Gil, The
Morse-Sard Theorem revisited, Quarterly J.
Math. 69 (2018), 887-913.
D. Azagra, J.
Ferrera and J. Gómez-Gil, Nonsmooth
Morse-Sard theorems, Nonlinear
Analysis 160 (2017), 53-69.
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.
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.
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:
D. Azagra, Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces, Studia Math. 125 (1997) no. 2, 179--186.
D. Azagra and R. Deville, James's theorem fails for starlike bodies in Banach spaces, J. Funct. Anal. 180 (2001), 328-346.
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.
D. Azagra and M. Jiménez-Sevilla, The failure of Rolle's theorem in infinite-dimensional Banach spaces, J. Funct. Anal. 182 (2001), 207-226.
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.
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.
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.
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.
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.