[lu]

Assistant Professor, Lakehead University

**Email:** *xlu8 AT lakeheadu.ca*

- P. Liu - X. Y. Lu (Submitted Paper)

Real order (an)-isotropic total variation in image processing - Part II: Learning of optimal structures (2019) - D. Wang - A. Rinaldo - X. Y. Lu (Submitted Paper)

DBSCAN: Optimal Rates For Density Based Clustering (2019) - R. Choksi - X. Y. Lu (Submitted Paper)

Bounds on the Geometric Complexity of Optimal Centroidal Voronoi Tesselations in 3D (2018) - P. Liu - X. Y. Lu (Submitted Paper)

Real order (an)-isotropic total variation in image processing - Part I: analytical analysis and functional properties (2018) - Y. Gao - J. G. Liu - X. Y. Lu - X. Xu (Accepted Paper:
*CVPDE*)

Maximal monotone operator in non-reflexive Banach space and the application to thin film equation in epitaxial growth on vicinal surface (2017) - X. Y. Lu (Accepted Paper:
*Commun. Math. Sci.*)

Analytical validation of a 2+1 dimensional continuum model for epitaxial growth with elastic substrate (2017) - Y. Gao - J. G. Liu - X. Y. Lu (Accepted Paper:
*ESAIM: COCV*)

Gradient flow approach to an exponential thin film equation: global existence and latent singularity (2017) - Y. Yu - D. Kamensky - M. C. Hsu - X. Y. Lu - Y. Bazilevs - T. J. R. Hughes (Accepted Paper:
*Math. Models Meth. Appl. Sci.*)

Error estimates for dynamic augmented Lagrangian boundary condition enforcement, with application to immersogeometric fluid–structure interaction (2017) - C. J. Garcia-Cervera - T. Giorgi - S. Joo - X. Y. Lu (Accepted Paper:
*SIAM J. Math. Anal.*)

Switching mechanism in the B_{1RevTilted} phase of bent-core liquid crystals (2017) - X. Y. Lu (Submitted Paper)

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

Regularity of optimal configurations for a model with perimeter-to-area ratio penalization. (2016) - J. Liu - X. Y. Lu - N. J. Walkington (Accepted Paper:
*Q. Appl. Math.*)

Analysis of a dislocation model for earthquakes (2016) - X. Y. Lu (Submitted Paper)

The regularization effect of Willmore energy (2016) - X. Y. Lu (
*J. Nonlinear Sci.*)

On the solutions of a 2+1 dimensional model for epitaxial growth with axial symmetry (2016) - X. Y. Lu (Accepted Paper:
*Netw. Heterog. Media*)

Regularity of densities in relaxed and penalized average distance problem (2015) - X. Y. Lu - D. Slepčev (Accepted Paper:
*ESAIM: COCV*)

Average-distance problem for parameterized curves (2015) - X. Y. Lu (Accepted Paper:
*Rend. Sem. Mat. Univ. Padova*)

Example of minimizer of the average distance problem with non closed set of corners (2015) - I. Fonseca - G. Leoni - X. Y. Lu (
*Commun. Part. Diff. Eq.*)

Regularity in time for weak solutions of a continuum model for epitaxial growth with elasticity on vicinal surfaces (2015) - X. Y. Lu (Accepted Paper:
*Adv. Calc. Var.*)

More counterexamples to regularity for minimizers of the average distance problem (2014) - X. Y. Lu - D. Slepčev (
*SIAM J. Math. Anal.*)

Properties of minimizers of average-distance problem via discrete approximation of measures (2013) - X. Y. Lu (Phd Thesis)

Geometric and regularity properties of solutions of some problems related to the average distance functional (2013) - X. Y. Lu (
*Commun. Math. Anal.*)

Geometric and topological properties of exponent related dynamic evolution (2012) - X. Y. Lu (Preprint)

Qualitative properties of evolution schemes in higher dimension domains (2012) - X. Y. Lu (
*Commun. Appl. Anal.*)

Branching time estimates in quasi-static evolution for the average distance functional (2011)