My research area is nonlinear partial differential equations. I am mainly interested in regularity issues and pattern formations for nonlinear PDEs coming from continuum mechanics and materials science.
Publications
- Yan, Xiaodong: Layer and stable solutions to a nonlocal model. Submitted.
- Niu, Xiaohua; Yan, Xiaodong: A phase field model for self-climb of prismatic dislocation loops. Submitted.
- Niu, Xiaohua; Xiang, Yang; Yan, Xiaodong: Well-posedness of a modified degenerate Cahn-Hilliard model for surface diffusion. Submitted.
- Chen, Ko-Shin; Muratov, Cyrill B; Yan, Xiaodong: Layered solutions for a nonlocal Ginzburg-Landau model with 1 periodic modulation. Submitted.
- Novack, Michael; Yan, Xiaodong: A smectic liquid crystal model in the periodic setting. Nonlinear Anal. 228 (2023), Paper No. 113187, 14 pp.
- Novack, Michael; Yan, Xiaodong: Nonlinear approximation of 3D smectic liquid crystals: sharp lower bound and compactness. Calc. Var. Partial Differential Equations 61 (2022), no. 4, Paper No. 157, 29 pp.
- Novack, Michael; Yan, Xiaodong Compactness and sharp lower bound for a 2D smectics model. J. Nonlinear Sci. 31 (2021), no. 3, Paper No. 60, 26 pp.
- Niu, Xiaohua; Xiang, Yang; Yan, Xiaodong: Phase field model for self-climb of prismatic dislocation loops by vacancy pipe diffusion. Int. J.Plasticity, 141, 102977, 2021.
- Xiang, Yang; Yan, Xiaodong Stability of dislocation networks of low angle grain boundaries using a continuum energy formulation. Discrete Contin. Dyn. Syst. Ser. B 23 (2018), no. 8, 2989–3021.
- Chen, Ko-Shin; Muratov, Cyrill B.; Yan, Xiaodong:Layer Solutions for a one dimensional nonlocal model of Ginzburg-Laudau type. Math. Model. Nat. Phenom. 12 (2017), no. 6, 68–90.
- Chen, Ko-Shin; Montenegro, Marcos; Yan, Xiaodong: The Brezis-Nirenberg problem for fractional elliptic operators. Math. Nachr. 290 (2017), no. 10, 1491–1511.
- Xiang, Yang; Yan, Xiaodong: Local stability of dislocation networks of low angle grain boundaries using a continuum energy formulation. Discrete Contin. Dyn. Syst. To appear.
- Muratov, Cyrill B.; Yan, Xiaodong: Uniqueness of one-dimensional Néel wall profiles. Proc. A. 472 (2016), no. 2187, 20150762, 15 pp.
- Arthur, Frank; Yan, Xiaodong: A Liouville-type theorem for higher order elliptic systems of Hénon-Lane-Emden type. Commun. Pure Appl. Anal. 15 (2016), no. 3, 807–830.
- Arthur, Frank; Yan, Xiaodong; Zhao, Mingfeng: A Liouville-type theorem for higher order elliptic systems. Discrete Contin. Dyn. Syst. 34 (2014), no.9, 3317-3339.
- Yan, Xiaodong: A Liouville-type theorem for higher order elliptic systems. J. Math. Anal. Appl. 387 (2012), no. 1, 153–165.
- Spirn, Daniel; Yan, Xiaodong: Uniqueness of stable Meissner state solutions of the Chern-Simons-Higgs energy. ESAIM Control Optim. Calc. Var. 16 (2010), no. 1, 23–36.
- Hang, Fengbo; Wang, Xiaodong; Yan, Xiaodong: An integral equation in conformal geometry. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 1, 1–21.
- Spirn, Daniel; Yan, Xiaodong: Minimizers near the first critical field for the nonself-dual Chern-Simons-Higgs energy. Calc. Var. Partial Differential Equations 35 (2009), no. 1, 1–37.
- Bevan, Jonathan; Yan, Xiaodong: Minimizers with topological singularities in two dimensional elasticity. ESAIM Control Optim. Calc. Var. 14 (2008), no. 1, 192–209.
- Hang, Fengbo; Wang, Xiaodong; Yan, Xiaodong: Sharp integral inequalities for harmonic functions. Comm. Pure Appl. Math. 61 (2008), no. 1, 54–95.
- Cho, Sungwon; Yan, Xiaodong: On the singular set for Lipschitzian critical points of polyconvex functionals. J. Math. Anal. Appl. 336 (2007), no. 1, 372–398.
- Yan, Xiaodong: Maximal smoothness for solutions to equilibrium equations in 2D nonlinear elasticity. Proc. Amer. Math. Soc. 135 (2007), no. 6, 1717–1724.
- Yan, Xiaodong: On limits to convective heat transport at infinite Prandtl number with or without rotation. J. Math. Phys. 45 (2004), no. 7, 2718–2743.
- Kohn, Robert V.; Yan, Xiaodong: Coarsening rates for models of multicomponent phase separation. Interfaces Free Bound. 6 (2004), no. 1, 135–149.
- Kohn, Robert V.; Yan, Xiaodong: Upper bound on the coarsening rate for an epitaxial growth model. Comm. Pure Appl. Math. 56 (2003), no. 11, 1549–1564.
- Lin, Fanghua; Yan, Xiaodong: A type of homogenization problem. Discrete Contin. Dyn. Syst. 9 (2003), no. 1, 1–30.
- Sverák, Vladimír; Yan, Xiaodong: Non-Lipschitz minimizers of smooth uniformly convex functionals. Proc. Natl. Acad. Sci. USA 99 (2002), no. 24, 15269–15276.
- Sverák, Vladimír; Yan, Xiaodong: A singular minimizer of a smooth strongly convex functional in three dimensions. Calc. Var. Partial Differential Equations 10 (2000), no. 3, 213–221.
- Yan, Xiaodong: Partial regularity of suitable weak solutions of complex Ginzburg Landau equations. Comm. Partial Differential Equations 24 (1999), no. 11-12, 2263–2277.