Xin Yang Lu's webpage!

Submitted papers

28

X.Y. Lu

J. Wei

Uniform bound on the number of partitions for optimal configurations of the Ohta-Kawasaki energy in 3D. (pdf)

Submitted
27

I. Fonseca

P. Liu

X.Y. Lu

Higher order Ambrosio-Tortorelli scheme with non-negative spatially dependent parameters.

Submitted

Published and accepted papers

26

Q. Du

X.Y. Lu

C. Wang

The average distance problem with perimeter-to-area ratio penalization. (pdf)

SIAM J. Math. Anal., in press
25

P. Liu

X.Y. Lu

W.L. Zhu

Adaptive image processing: a bilevel structure learning approach for mixed-order total variation regularizers.

Commun. Math. Sci., in press
24

X.Y. Lu

X. Xu

W. Zhang

Blowup rate estimates of a singular potential and its gradient in the Landau-de Gennes theory. (pdf)

J. Nonlinear Sci., in press
23

Q. Du

X.Y. Lu

C. Wang

The average distance problem with an Euler elastica penalization. (pdf)

Interfaces Free. Boundaries, in press
22

Y. Liu

X.Y. Lu

X. Xu

Regularity of a gradient flow generated by the anisotropic Landau-de Gennes energy with a singular potential. (pdf)

SIAM J. Math. Anal., 53(3) (2021) 3338-3365.
21

Y. Gao

X.Y. Lu

C. Wang

Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects. (pdf)

Adv. Calc. Var., (2021) pp. 000010151520200114.
20

X.Y. Lu

D. Slepčev

Average-distance problem with curvature penalization for data parameterization: regularity of minimizers. (pdf)

ESAIM: Control Optim. Calc. Var., 27(8) (2021).
19

R. Choksi

X.Y. Lu

Bounds on the Geometric Complexity of Optimal Centroidal Voronoi Tesselations in 3D. (pdf)

Commun. Math. Phys., 277(2) (2020).
18

S. Alama

L. Bronsard

X.Y. Lu

C. Wang

Periodic minimizers of a ternary non-local isoperimetric problem. (pdf)

Indiana Univ. Math. J., 70(6) (2021).
17

H. You

X.Y. Lu

N. Trask

Y. Yu

An Asymptotically Compatible Approach For Neumann-Type Boundary Condition On Nonlocal Problems. (pdf)

ESAIM: Mathematical Modelling and Numerical Analysis, 54 (2020) 1373-1413.
16

D. Wang

X.Y. Lu

A. Rinaldo

DBSCAN: Optimal Rates For Density Based Clustering. (pdf)

Journal of Machine Learning Research (JMLR), 20(170) (2019) 1-50.
15

Y. Gao

J.-G. Liu

X.Y. Lu

Gradient flow approach to an exponential thin film equation: global existence and latent singularity. (pdf)

ESAIM: Control Optim. Calc. Var., 25:49 (2019).
14

C.J. Garcia-Cerveira

T. Giorgi

S. Joo

X.Y. Lu

Switching mechanism in the $B_{1RevTilted}$ phase of bent-core liquid crystals. (pdf)

SIAM J. Math. Anal., 50(5) (2018) 4889-4913.
13

X.Y. Lu

Analytical validation of a 2+1 dimensional continuum model for epitaxial growth with elastic substrate. (pdf)

Commun. Math. Sci., 16(5) (2018) 1379-1394.
12

Y. Yu

D. Kamensky

M.-C. Hsu

X.Y. Lu

Y. Bazilevs

T.J.R. Hughes

Error estimates for projection-based dynamic augmented Lagrangian boundary condition enforcement, with application to fluid–structure interaction. (pdf)

Math. Models Meth. Appl. Sci., 28(12) (2018) 2457-2509.
11

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. (pdf)

Calc. Var. Partial Differential Equations, 57(2) (2018).
10

X.Y. Lu

On the solutions of a 2+1 dimensional model for epitaxial growth with axial symmetry. (pdf)

J. Nonlinear Sci., 28(2) (2018) 807-831.
9

X.Y. Lu

Example of minimizer of the average distance problem with non closed set of corners. (pdf)

Rend. Sem. Mat. Univ. Padova, 137 (2017) 19-55.
8

J. Liu

X.Y. Lu

N. J. Walkington

Analysis of a dislocation model for earthquakes.(pdf)

Q. Appl. Math., 74-4 (2016) 765-786.
7

X.Y. Lu

D. Slepčev

Average-distance problem for parameterized curves. (pdf)

ESAIM: Control Optim. Calc. Var., 22-2 (2016) 404-416.
6

X.Y. Lu

Regularity of densities in relaxed and penalized average distance problem. (pdf)

Netw. Heterog. Med., 10-4 (2015) 837-855.
5

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. (pdf)

Commun. Part. Diff. Eq., 40-10 (2015) 1942-1957.
4

X.Y. Lu

More counterexamples to regularity for minimizers of the average-distance problem. (pdf)

Adv. Calc. Var. , 9-1 (2015) 41-63.
3

X.Y. Lu

D. Slepčev

Properties of minimizers of average distance problem via discrete approximation of measures. (pdf)

SIAM J. Math. Anal., 45-5 (2013) 3114-3131.
2

X.Y. Lu

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

Commun. Appl. Anal., 16-2 (2012) 229-248.
1

X.Y. Lu

Geometric and topological properties of exponent related dynamic evolution. (pdf)

Commun. Math. Anal., 12-2 (2012) 106-123.

Theses

1

X.Y. Lu

Geometric and regularity properties of solutions of some problems related to the average distance functional. (pdf)

PhD Thesis (in English).