X. Y. Lu:
Branching time estimates in quasi-static evolution for the average distance functional
Commun. Appl. Anal. Vol. 16, N. 2, p. 229-248, 2011

X. Y. Lu:
Geometric and topological properties of exponent related dynamic evolution
Commun. Math. Anal. Vol. 12, N. 2, p. 106-123, 2012

X. Y. Lu:
Qualitative properties of evolution schemes in higher dimension domains
(Preprint) 2012

X. Y. Lu, D. Slepev:
Properties of minimizers of average-distance problem via discrete approximation of measures
SIAM J. Math. Anal. Vol. 45, N. 5, p. 3114-3131, 2013

X. Y. Lu:
Geometric and regularity properties of solutions of some problems related to the average distance functional
(Phd Thesis) 2013

X. Y. Lu:
More counterexamples to regularity for minimizers of the average distance problem
Adv. Calc. Var. (Accepted Paper) 2014

X. Y. Lu:
Regularity of densities in relaxed and penalized average distance problem
Netw. Heterog. Media (Accepted Paper) 2015

X. Y. Lu, D. Slepev:
Average-distance problem for parameterized curves
ESAIM: COCV (Accepted Paper) 2015

X. Y. Lu:
Example of minimizer of the average distance problem with non closed set of corners
Rend. Sem. Mat. Univ. Padova (Accepted Paper) 2015

I. Fonseca, G. Leoni, X. Y. Lu:
Regularity in time for weak solutions of a continuum model for epitaxial growth with elasticity on vicinal surfaces
Commun. Part. Diff. Eq. Vol. 40, N. 10, p. 1942-1957, 2015

X. Y. Lu:
Strong solutions of a continuum model for epitaxial growth with elasticity on vicinal surfaces.
(Submitted Paper) 2016

J. Liu, X. Y. Lu, N. J. Walkington:
Analysis of a dislocation model for earthquakes 
Q. Appl. Math. (Accepted Paper) 2016

X. Y. Lu:
On the solutions of a 2+1 dimensional model for epitaxial growth with axial symmetry
J. Nonlinear Sci. 2016

Y. Gao, J. G. Liu, X. Y. Lu, X. Xu:
Maximal monotone operator in non-reflexive Banach space and the application to thin film equation in epitaxial growth on vicinal surface
CVPDE (Accepted Paper) 2017

Y. Gao, J. G. Liu, X. Y. Lu:
Gradient flow approach to an exponential thin film equation: global existence and latent singularity
ESAIM: COCV (Accepted Paper) 2017

Y. Bazilevs, M. C. Hsu, T. J. R. Hughes, D. Kamensky, X. Y. Lu, Y. Yu:
Error estimates for dynamic augmented Lagrangian boundary condition enforcement, with application to immersogeometric fluidstructure interaction
Math. Models Meth. Appl. Sci. (Accepted Paper) 2017

C. J. Garcia-Cervera, T. Giorgi, S. Joo, X. Y. Lu:
Switching mechanism in the B_{1RevTilted} phase of bent-core liquid crystals
SIAM J. Math. Anal. (Accepted Paper) 2017

X. Y. Lu:
Analytical validation of a 2+1 dimensional continuum model for epitaxial growth with elastic substrate
Commun. Math. Sci. (Accepted Paper) 2017

R. Choksi, X. Y. Lu:
Bounds on the Geometric Complexity of Optimal Centroidal Voronoi  Tesselations in 3D
(Submitted Paper) 2018

P. Liu, X. Y. Lu:
Real order (an)-isotropic total variation in image processing - Part I:  analytical analysis and functional properties
(Submitted Paper) 2018

X. Y. Lu, A. Rinaldo, D. Wang:
DBSCAN: Optimal Rates For Density Based Clustering
(Submitted Paper) 2019

P. Liu, X. Y. Lu:
Real order (an)-isotropic total variation in image processing - Part II:  Learning of optimal structures
(Submitted Paper) 2019