Affiliation

Research interests

• Nonlinear partial differential equations, especially elliptic and parabolic equations

• Potential theory

Publications

1. Nonlinear parabolic capacity and polar sets of superparabolic functions. To appear in Math. Ann. (with J. Kinnunen, R. Korte, M. Parviainen)
2. New perturbation methods for nonlinear parabolic problems To appear in J. Math. Pures Appl. (9) (with G. Mingione)
3. Gradient regularity for nonlinear parabolic equations. To appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) (with G. Mingione)
4. Local Hölder continuity for doubly nonlinear parabolic equations. To appear in Indiana Univ. Math. J. (with J. Siljander, J.-M. Urbano)
5. Hölder continuity for Trudinger's equation in measure spaces. To appear in Calc. Var. Partial Differential Equations (with R. Laleoglu, J. Siljander, J.-M. Urbano)
6. Pointwise gradient estimates. To appear in Nonlinear Anal. (with G. Mingione)
7. Universal potential estimates. J. Funct. Anal. 262:4205-4269, 2012 (with G. Mingione)
8. Potential estimates and gradient boundedness for nonlinear parabolic systems. Rev. Mat. Iberoam. 28:535-576, 2012 (with G. Mingione)
9. A surprising linear type estimate for nonlinear elliptic equations. C. R. Math. Acad. Sci. Paris. 349(15-16):889-892, 2011 (with G. Mingione)
10. Superharmonic functions are locally renormalized solutions. Ann. Inst. H. Poincaré Anal. Non Linéaire 28:775-795, 2011 (with T. Kilpeläinen, A. Tuhola-Kujanpää)
11. Endpoint and intermediate potential estimates for nonlinear equations. Boll. Unione Mat. Ital. (9) 4(1):149-157, 2011 (with G. Mingione)
12. Nonlinear potential estimates in parabolic problems. Rend. Lincei Mat. Appl. 22:1-14, 2011 (with G. Mingione)
13. A note on the Wolff potential estimate for solutions to elliptic equations involving measures. Preprint Adv. Calc. Var. 3(1): 99-113, 2010 (with R. Korte)
14. A connection between a general class of superparabolic functions and supersolutions. Preprint J. Evol. Eq. 10(1):1-20, 2010 (with R. Korte, and M. Parviainen)
15. Lower semicontinuity of weak supersolutions to nonlinear parabolic equations. Preprint. Differential Integral Equations, 22(11-12):1211-1222, 2009
16. Obstacle problem for nonlinear parabolic equations. Preprint. J. Differential Equations, 246(9):3668-3680, 2009 (with R. Korte, and J. Siljander)
17. Existence of solutions to degenerate Cauchy problems. Preprint. Manuscripta Math., 128(2):213-249, 2009 (with M. Parviainen)
18. The weak Harnack estimate for weak supersolutions to nonlinear degenerate parabolic equations. Preprint. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), 7(4):673-716, 2008.
19. Harnack's inequality for quasiminimizers with non-standard growth conditions. Preprint. J. Math. Anal. Appl., 344(1), 504-520, 2008. (with P. Harjulehto, T. Lukkari, N. Marola, and M. Parviainen)
20. Local behaviour of solutions to doubly nonlinear parabolic equations. Preprint. Math. Ann., 337(3):705-728, 2007. (with J. Kinnunen)


21. Harnack estimates for supersolutions to a nonlinear degenerate parabolic equation. PhD Thesis, Report A532, Helsinki University of Technology, Institute of Mathematics, 2007.
22. Väitöstutkimuksia epälineaarisista parabolisista yhtälöistä ja systeemeistä, Preprint of the popular article, Arkhimedes, 1, 2008. (with M. Parviainen)

Research groups

• Nonlinear PDE group

• Vectorial problems

Conferences

• Spring school in harmonic analysis and PDE 2008

• WCNA-2008

• Function spaces, Differential Operators and Nonlinear Analysis

Contact

• E-mail: tuomo.kuusitkk.fi

• Contact information at Aalto University