PUBLICATIONS

PUBLICATIONS

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MATHEMATICS - Books

1. Armstrong S. & Kuusi T.: Elliptic homogenization from qualitative to quantitative. Preprint

2. Armstrong S. & Kuusi T. & Mourrat J.-C.: Quantitative stochastic homogenization and large-scale regularity. Grundlehren der Mathematischen Wissenschaften 352. Springer, Cham, 2019. xxxviii+518 pp.  Book, Preprint

3. Palatucci, G. (Ed.) & Kuusi, T. (Ed.): Recent Developments in Nonlocal Theory. Berlin: Sciendo (2018).  Book

MATHEMATICS - Published, accepted

1. Armstrong S. & Kuusi T. : Renormalization group and elliptic homogenization in high contrast,  Invent. Math. (2025, to appear).  Article, Preprint 

2. Avelin, B. & Kuusi, T. & Nummi, P. &  Saksman, E. & Tölle, J. & Viitasaari, L.: Renormalized stochastic pressure equation with log-correlated Gaussian coefficients,  J. Differential Equations 439 (2025), Paper No. 113416. Article 

3. Aleksanyan, G. & Kuusi, T.: Quantitative Homogenization for the Obstacle Problem and Its Free Boundary. Arch Rational Mech Anal 248, 71 (2024).   Article 

4. Armstrong S. & Kuusi T.  & Smart C.: Large-scale analyticity and unique continuation for periodic elliptic equations. Comm. Pure Appl. Math  76, 1, 73-113 (2023).  Article, Preprint

5. Armstrong S. & Hannukainen A. & Kuusi T. & Mourrat J.-C.: An iterative method for elliptic problems with rapidly oscillating coefficients. ESAIM: Math. Model. Num. 55(1) (2021), 37-55.  Article,  Preprint 

6. Kuusi T & Misawa M. & Nakamura K. : Global existence for the p-Sobolev flow. J. Differential Equations 279(5) (2021), 245-281. Article,  Preprint 

7. Armstrong S. & Ferguson S. & Kuusi T. : Higher-Order Linearization and Regularity in Nonlinear Homogenization. Arch. Rat. Mech. Anal. 237 (2020), 631–741. Article

8. Kuusi T & Misawa M. & Nakamura K. : Regularity estimates for the p-Sobolev flow. J.  Geom. Anal. 30 (2) (2020), 1918-1964. Article,

9. Armstrong S. & Ferguson S. & Kuusi T. : Homogenization, Linearization, and Large-Scale Regularity for Nonlinear Elliptic Equations. Comm. Pure Appl. Math., 74 (2021), 286-365. Article, Preprint

10. Avelin B. & Kuusi T. & Nyström K.: Boundary behavior of solutions to the parabolic p-Laplace equation. Anal. PDE 12(1) (2019), 1–42. Article, Preprint

11. Kuusi T. & Mingione G.: Vectorial nonlinear potential theory. J. Eur. Math. Soc. 20(4) (2018), 929–1004.  Article, Preprint

12. Baroni P. & Kuusi T. & Lindfors C. & Urbano J.-M.: Existence and boundary regularity for degenerate phase transitions. SIAM J. Math. Anal., 50(1) (2018), 456–490.   Article,  Preprint 

13. Avelin B. & Kuusi T. & Mingione G.: Nonlinear Calderón-Zygmund theory in the limiting case. Arch. Rat. Mech. Anal. 227(2) (2018), 663–714.  Article, Preprint

14. Breit D. & Cianchi A. &  Diening L. & Kuusi T. & Schwarzacher S.: Pointwise Calderon-Zygmund gradient estimates for the p-Laplace system. J. Math. Pures Appl. 114 (2018), 146-190.  Article, Preprint 

15. Armstrong S. & Kuusi T. & Mourrat J.-C. & Prange C.: Quantitative analysis of boundary layers in periodic homogenization. Arch. Rat. Mech. Anal. 226(2) (2017), 695–741. Article, Preprint

16. Korvepää J. & Kuusi T. & Palatucci G.: Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations. Math. Ann. 369(3-4) (2017), 1443–1489. Article, Preprint

17. Korvepää J. & Kuusi T. & Lindgren E.: Equivalence of solutions to fractional p-Laplace type equations. J. Math. Pures Appl., to appear. Article, Preprint 

18. Armstrong S. & Kuusi T. & Mourrat J.-C.: The additive structure of elliptic homogenization. Invent. Math. 208(3) (2017), 999-1154. Article, Preprint

19. Korvepää J. & Kuusi T. & Palatucci G.: The obstacle problem for nonlinear integro-differential operators. Calc. Var. Partial Differential Equations 55(3), (2016). Article, Preprint

20. Kuusi T. & Mingione G.: Partial regularity and potentials.  J. Éc. Polytech. Math. 3 (2016), 309-363. Article

21. Armstrong S. & Gloria A. & Kuusi T.: Bounded correctors in almost periodic homogenization. Arch. Rat. Mech. Anal. 222(1) (2016), 393-426. Article, Preprint

22. Armstrong S. & Kuusi T. & Mourrat J.-C.: Mesoscopic higher regularity and subadditivity in elliptic homogenization. Comm. Math. Phys., 347 (2016), 315–361. Article, Preprint

23. Di Castro A. & Kuusi T. & Palatucci G.: Local behavior of fractional p-minimizers. Ann. Inst. H. Poincaré Anal. Non Linéaire 33(5) (2016), 1279–1299. Article, Preprint

24. Kuusi T. & Lindqvist P. & Parviainen M.: Shadows of infinities. Ann. Mat. Pura Appl., 195(4) (2016), 1185–1206. Article, Preprint

25. Kuusi T. & Monsaingeon L., & Videman J.: Systems of partial differential equations in porous medium. Nonlinear Analysis TMA 133(1) (2106), 79-101. Article, Preprint

26. Kuusi T. & Mingione G. & Sire Y.: Nonlocal equations with measure data. Comm. Math. Phys. 337 (2015), 1317-1368. Article, Preprint

27. Avelin B. & Kuusi T. & Parviainen M.: Variational parabolic capacity. Discrete Contin. Dyn. Syst. 35(12) (2015), 5665-5688. Article, Preprint

28. Kuusi T. & Mingione G. & Sire Y.: Nonlocal self-improving properties. Anal. PDE 8 (2015) 57-114. Article, Preprint

29. Baroni P. & Kuusi T. & Mingione G.: Borderline gradient continuity of minima. J. Fixed Point Theory Appl. 15 (2014) 537-575.  Article, Preprint

30. Kuusi T. & Mingione G.: A nonlinear Stein theorem. Calc. Var. Partial Differential Equations 51 (2014), 45-86.  Article, Preprint

31. Di Castro A. & Kuusi T. & Palatucci G.: Nonlocal Harnack inequalities. J. Funct. Anal. 267 (2014), 1807-1836.   Article, Preprint

32. Kuusi T. & Mingione G., Nyström, K.: A boundary Harnack inequality for singular equations of p-parabolic type, Proc. Amer. Math. Soc. 142(8) (2014), 2705-2719.  Article, Preprint

33. Kuusi T. & Mingione G.: Borderline gradient continuity for nonlinear parabolic systems. Math. Ann. 360(3-4) (2014), 937–993.  Article, Preprint

34. Baroni P. & Kuusi T. & Urbano J.M.:  A quantitative modulus of continuity for the two-phase Stefan problem. Arch. Rat. Mech. Anal., 214 (2) (2014), 545-573. Article, Preprint

35. Kuusi T. & Mingione G.: Guide to nonlinear potential estimates. Bull. Math. Sci. 4(1) (2014), 1-82. Article

36. Kuusi T. & Mingione G.: Riesz potentials and nonlinear parabolic equations. Arch. Rat. Mech. Anal. 212 (2014), 727-780. Article, Preprint

37. Kuusi T. & Mingione G.: The Wolff gradient bound for degenerate parabolic equations. J. Eur. Math. Soc. 16(4) (2014), 835-892. Article, Preprint

38. Kuusi T. & Mingione G. & Nyström K.: Sharp regularity for evolutionary obstacle problems, interpolative geometries and removable sets, J. Math. Pures Appl. (9) 101(2) (2014), 119-151. Article, Preprint

39. Daskalopoulos P. & Kuusi T. & Mingione G.: Borderline estimates for fully nonlinear elliptic equations. Comm. Partial Differential Equations 39(3) (2014), 574-590. Article, Preprint

40. Kuusi T. & Mingione G.: Gradient regularity for nonlinear parabolic equations. Ann. Sc. Norm. Super. Pisa Cl. Sci. (V) 12 (2013), 755-822. Article, Preprint

41. Kuusi T. & Mingione G.: Linear potentials in nonlinear potential theory. Arch. Rat. Mech. Anal. 207(1) (2013), 215–246. Article, Preprint

42. Kinnunen J. & Korte R. & Kuusi T. & Parviainen M.: Nonlinear parabolic capacity and polar sets of superparabolic functions. Math. Ann. 355(4) (2013), 1349–1381. Article, Preprint

43. Kuusi T. & Mingione G.: New perturbation methods for nonlinear parabolic systems. J. Math. Pures Appl. (9) 98(4) (2012), 390-427. Article, Preprint

44. Kuusi T. & Siljander J. & Urbano J.-M.: Local Hölder continuity for doubly nonlinear parabolic equations. Indiana Univ. Math. J. 61(1) (2012), 399–430. Article, Preprint

45. Kuusi, T. & Mingione G.: Universal potential estimates. J. Funct. Anal. 262 (2012), 4205-4269. Article, Preprint

46. Kuusi T. & Laleoglu R. & Siljander J. & Urbano J.-M.: Hölder continuity for Trudinger's equation in measure spaces. Calc. Var. Partial Differential Equations 45(1-2) (2012), 193-229. Article, Preprint

47. Kuusi T. & Mingione G.: Potential estimates and gradient boundedness for nonlinear parabolic systems. Rev. Mat. Iberoamericana 28(2012), 535-576. Article, Preprint

48. Kuusi T. & Kilpeläinen T. & Tuhola-Kujanpää A.: Superharmonic functions are locally renormalized solutions. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), 775-795. Article, Preprint

49. Korte R. & Kuusi T. & Parviainen M.: A connection between a general class of superparabolic functions and supersolutions, J. Evol. Equ. 10(1) (2010), 1-20. Article, Preprint

50. Korte R. & Kuusi T.: A note on the Wolff potential estimate for solutions to elliptic equations involving measures. Adv. Calc. Var. 3 (2010), 99-113. Article, Preprint

51. Korte R. & Kuusi T. & Siljander J.: Obstacle problem for nonlinear parabolic equations. J. Differential Equations 246(9) (2009), 3668-3680. Article, Preprint

52. Kuusi T.: Lower semicontinuity of weak supersolutions to a nonlinear parabolic equation. Differential Integral Equations 22(11-12) (2009), 1211-1222. Article, Preprint

53. Kuusi T. & Parviainen M.: Existence of solutions to degenerate Cauchy problems, Manuscripta Math. 128 (2009), 213-249. Article, Preprint

54. Kuusi T.: Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations. Ann. Sc. Norm. Super. Pisa Cl. Sci. (V) 7 (2008), 673-716. Article, Preprint

55. Harjulehto P. & Kuusi T. & Lukkari T. & Marola N . & Parviainen M.: Harnack's inequality for quasiminimizers with nonstandard growth conditions. J. Math. Anal. Appl. 344(1) (2008), 504-520. Article, Preprint

56. Kinnunen J. & Kuusi T.: Local behavior of solutions to doubly nonlinear parabolic equations. Math. Ann. 337(3) (2007), 705-728. Article, Preprint

MATHEMATICS - Surveys, announcements, short notes

1. Breit D. & Cianchi A. &  Diening L. & Kuusi T. & Schwarzacher S.: The p-Laplace system with right-hand side in divergence form: Inner and up to the boundary pointwise estimates. Nonlinear Analysis TMA 153 (2017), 200–212. Article

2. Korvepää J. & Kuusi T. & Palatucci G.: A note on fractional supersolutions. Electron. J. Differential Equations, 263 (2016), 1–9. Preprint 

3. Korvepää J. & Kuusi T. & Palatucci G.: Hölder continuity up to the boundary for a class of fractional obstacle problems. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 27(3) (2016), 355–367. Preprint

4. Kuusi T. & Mingione G.: Nonlinear Potential Theory of elliptic systems., Nonlinear Analysis TMA 138 (2016), 277–299. Preprint

5. Kuusi T. & Mingione G. & Sire Y.: A fractional Gehring lemma, with applications to nonlocal equations, Rend. Lincei Mat. Appl. 25(4) (2014), 345–358. Preprint

6. Kuusi, T. & Mingione G.: Pointwise gradient estimates. Nonlinear Analysis TMA 75 (2012), 4650-4663. Preprint

7. Kuusi T. & Mingione G.: A surprising linear type estimate for nonlinear elliptic equations. C. R. Math. Acad. Sci. Paris, Ser. I 349 (2011), 889-892. 

8. Kuusi T. & Mingione G.: Endpoint and intermediate potential estimates for nonlinear equations. Boll. Unione Mat. Ital. (9) 4(1) (2011), 149-157. 

9. Kuusi T. & Mingione G.: Nonlinear potential estimates in parabolic problems. Rend. Lincei Mat. Appl. 22 (2011), 1-14.

PHD THESIS

1. Harnack estimates for supersolutions to a nonlinear degenerate parabolic equation. Report A532, Helsinki University of Technology, Institute of Mathematics, 2007.

MEDICINE

1. Fagerlund, Heikkinen, Autti-Rämö, Korkman, Timonen, Kuusi, Riley, Lundbom, N.: Brain metabolic alterations in adolescents and young adults with fetal alcohol spectrum disorders. Alcoholism: Clinical and Experimental Research 30(12) (2006), 2097-2104.

2. Urrila, Hakkarainen, Heikkinen, Huhdankoski, Kuusi, Stenberg, Häkkinen, Porkka-Heiskanen, Lundbom: Preliminary findings of proton magnetic resonance spectroscopy in occipital cortex during sleep deprivation. Psychiatry Research-Neuroimaging 147(1) (2006), 41-46.

3. Linnankivi, Lundbom, Autti, Häkkinen, Koillinen, Kuusi, Lönnqvist, Sainio, Valanne, Äärimaa, Pihko: Five new cases of a recently described leukoencephalopathy with high brain lactate. Neurology 63(4) (2004), 688-692.