Publications

Published/Accepted:

1. Ugo Gianazza, Naian Liao, Continuity of the temperature in a multi-phase transition problem. Part III, J. d’Analyse Math., 150(2), (2023), 583–607.

2. Verena Bögelein, Frank Duzaar, Naian Liao, Leah Schätzler, On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II, Rev. Mat. Iberoam., 39(3), (2023),1005-1037.

3. Verena Bögelein, Frank Duzaar, Naian Liao, Christoph Scheven, Gradient Hölder regularity for degenerate parabolic systems, Nonlinear Anal., 225 (2022), Paper No. 113119, 61 pp.

4. Naian Liao, On the logarithmic type boundary modulus of continuity for the Stefan problem: To the memory of Emmanuele DiBenedetto, Adv. Math., 408, (2022), Paper No. 108613, 53 pp.

5. Naian Liao, Local continuity of weak solutions to the Stefan problem involving the singular p-Laplacian, SIAM J. Math. Anal., 54(2), (2022), 2570-2586.

6. Naian Liao, Leah Schätzler, On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part III,  Int. Math. Res. Not. IMRN, 2022(3), (2022), 2376-2400.

7. Verena Bögelein, Frank Duzaar, Naian Liao, Christoph Scheven, Boundary regularity for parabolic systems in convex domains,  J. Lond. Math. Soc. (2), 105(3), 1702-1751.

8. Ugo Gianazza, Naian Liao, Continuity of the temperature in a multi-phase transition problem, Math. Ann., 384(1-2), (2022), 211-245.

9. Ugo Gianazza, Naian Liao, A boundary estimate for singular sub-critical parabolic equations, Int. Math. Res. Not. IMRN, 2022(10), (2022), 7332-7353.

10. Naian Liao, Regularity of weak supersolutions to elliptic and parabolic equations: Lower semicontinuity and pointwise behavior, J. Math. Pures Appl. (9), 147, (2021), 179-204.

11. Naian Liao, Remarks on parabolic De Giorgi classes, Ann. Mat. Pura Appl. (4), 200(6), (2021), 2361-2384.

12. Naian Liao, Hölder regularity for porous medium systems, Calc. Var. Partial Differential Equations, 60(4), (2021),  Paper No. 156, 28 pp. 

13. Verena Bögelein, Frank Duzaar, Naian Liao, On the Hölder regularity of signed solutions to a doubly nonlinear equation, J. Funct. Anal., 281(9), (2021),   Paper No. 109173, 58 pp.

14. Naian Liao, Igor I. Skrypnik, Vincenzo Vespri, Local regularity for an anisotropic elliptic equation, Calc. Var. Partial Differential Equations, 59, (2020), Article No. 116, 31 pp.

15. Ugo Gianazza, Naian Liao, A boundary estimate for degenerate parabolic diffusion equations, Potential Anal., (53)3, (2020), 977-995.

16. Naian Liao, A unified approach to the Hölder regularity of solutions to degenerate and singular parabolic equations, J. Differential Equations, 268(10), (2020), 5704–5750.

17. Naian Liao, A sufficient condition for the continuity of solutions to a logarithmic diffusion equation, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 19(3), (2019), 1161–1184.

18. Ugo Gianazza, Naian Liao, Teemu Lukkari, A boundary estimate for singular parabolic diffusion equations, NoDEA Nonlinear Differential Equations Appl., 25, Art. 33, (2018), 24pp.

19. Colin Klaus, Naian Liao, A short proof of Hölder continuity for functions in DeGiorgi classes, Ann. Acad. Sci. Fenn. Math., 43, (2018), 931–934. 

20. Naian Liao, Existence and non-existence of solutions to a logarithmic diffusion equation in bounded domains, Manuscripta Math., 147(1), (2015), 101–138. 

21. Emmanuele DiBenedetto, Ugo Gianazza, Naian Liao, Two remarks on the local behavior of logarithmically singular diffusion equations, Riv. Math. Univ. Parma (N.S.), 5(1), (2014), 139–182. 

22. Emmanuele DiBenedetto, Ugo Gianazza, Naian Liao, Logarithmically singular parabolic equations as limits of the porous medium equation, Nonlinear Anal., 75(12), (2012), 4513–4533. 

23. Emmanuele DiBenedetto, Ugo Gianazza, Naian Liao, On the local behavior of non-negative solutions to a logarithmically singular equation, Discrete Contin. Dyn. Sys. Ser. B, 17(6), (2012), 1841–1858. 

Submitted:

1. Verena Bögelein, Frank Duzaar, Ugo Gianazza, Naian Liao, Christoph Scheven, Hölder continuity of the gradient of solutions to doubly nonlinear equations, arXiv:2305:08539

2. Ugo Gianazza, Naian Liao, Continuity of the temperature in a multi-phase transition problem. Part II, preprint.

3. Naian Liao, Hölder regularity for parabolic fractional p-Laplacian, arXiv:2205.10111