• Postdoctoral researcher at Aalto University School of Science and Technology (former Helsinki University of Technology (TKK))
  
  
• Contact information

Research interests

• nonlinear partial differential equations (parabolic, in particular), stochastic game theory, calculus of variations, nonlinear potential theory, analysis on metric spaces.

Research papers

1. Irregular time dependent obstacles (with P. Lindqvist). Preprint at arXiv.
   

2. Nonhomogeneous variational problems and quasi-minimizers on metric spaces (with J. Gong and J.J. Manfredi). Submitted. Preprint at arXiv.
   

3. Equivalence of viscosity and weak solutions for the p(x)-Laplacian (with P. Juutinen and T. Lukkari). Ann. Inst. H. Poincaré Anal. Non Linéaire. 27(6):1471-1487, 2010. Preprint pdf.
   

4. An asymptotic mean value characterization for a class of nonlinear parabolic equations related to tug-of-war games (with J.J. Manfredi and J.D. Rossi). SIAM J. Math. Anal. 42(5):2058-2081, 2010. Preprint pdf.
   

5. Dynamic programming principle for tug-of-war games with noise (with J.J. Manfredi and J.D. Rossi). To appear in ESAIM Control Optim. Calc. Var. Preprint pdf.
   

6. On the definition and properties of p-harmonious functions (with J.J. Manfredi and J.D. Rossi). To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. Preprint pdf.
   

7. An existence result for superparabolic functions (with J. Kinnunen and T. Lukkari), J. Funct. Anal. 258:713-728, 2010. Preprint pdf.
   

8. An asymptotic mean value characterization for p-harmonic functions (with J.J. Manfredi and J.D. Rossi). Proc. Amer. Math. Soc. 138(3):881-889, 2010. Preprint pdf.
   

9. Stability for degenerate parabolic equations (with J. Kinnunen), Adv. Calc. Var. 3(1):29-48, 2010. Preprint pdf.
   

10. Self-improving property of nonlinear higher order parabolic systems near the boundary (with V. Bögelein), NoDEA Nonlinear Differential Equations Appl. 17(1):21-54, 2010. Preprint pdf.
    

11. Existence for a degenerate Cauchy problem (with T. Kuusi), Manuscripta Math. 128(2):213-249, 2009. Preprint pdf.
    

12. Lebesgue points and the fundamental convergence theorem for superharmonic functions (with A. Björn, and J. Björn), Rev. Mat. Iberoam. 26(1):147-174, 2010. Preprint pdf.
    

13. Nonlinear balayage on metric spaces (with A. Björn, J. Björn, and T. Mäkäläinen), Nonlinear Anal. 71(5-6):2153-2171, 2009. Preprint pdf.
    

14. A connection between a general class of superparabolic functions and supersolutions (with R. Korte, and T. Kuusi), J. Evol. Equ. 10(1):1-20, 2010. Preprint pdf
    

15. Reverse Hölder inequalities for singular parabolic equations near the boundary, J. Differential Equations 246:512-540, 2009. Preprint pdf.
    

16. Global gradient estimates for degenerate parabolic equations in nonsmooth domains, Ann. Mat. Pura Appl. 188(2):333-358, 2009. Preprint pdf.
    

17. Harnack's inequality for quasiminimizers with non-standard growth conditions (with P. Harjulehto, T. Kuusi, T. Lukkari, and N. Marola), J. Math. Anal. Appl. 344(1): 504-520, 2008. Preprint pdf.
    

18. Global higher integrability for parabolic quasiminimizers in nonsmooth domains, Calc. Var. Partial Differential Equations 31(1):75-98, 2008.

Other:

1. Väitöstutkimuksia epälineaarisista parabolisista yhtälöistä ja systeemeistä (with T. Kuusi), Arkhimedes, 1/2008. pdf.

2. Global higher integrability for nonlinear parabolic partial differential equations in nonsmooth domains, Dissertation, Helsinki University of Technology, Institute of Mathematics, 2007. pdf.

Research group

• Nonlinear PDE group.

Teaching

• Mat-1.C Harmonic Analysis, fall 2010.
  
  Tuesday lecture moves to U322, at 8-10 am.
  
  Course description. Grading
  Lectures
  
  • 1. lecture
  • 2. lecture
  • 3. lecture
  • 4. lecture
  • 5. lecture
  • 6. lecture
  • 7. lecture
  • 8. lecture
  • 9. lecture
  • 10. lecture
  • 11. lecture
  • 12. lecture
  • first part lectures
  Exercises
  
  • 1. exercise
  • 2. exercise
  • 3. exercise
  • 4. exercise
  • 5. exercise
  • 6. exercise
  
  

• Lecturer 2008, Basic course in Mathematics S2, Mat-1.1220 (series, analytic geometry, functions of several variables);
• Lecturer 2007, Basic course in Mathematics L3, Mat-1.1030 (complex analysis, linear algebra);
• Basic course in Mathematics L4, Mat-1.404, (PDEs);
• Finite Difference Methods, Mat-1.169, (numerical methods in PDEs).

Conferences and research visits

• The Jyväskylä summer school, Jyväskylä.
• Nonlinear Problems in PDEs, Parma.
• Research visit, Trondheim.
• Research visit, Köln.
• Finnish Mathematical Days, Jyväskylä, 4.1.-5.1.2010
  
• SIAM Conference on Analysis of Partial Differential Equations, Miami, 6.-10.12.2009.
• Research visit, Pittsburgh.
  
• Research visit, Jyväskylä.
  
• Intensive research period: Regularity for non-linear PDEs, Pisa, 13.-19.9.2009.
• The 2008-2009 academic year, Fulbright Scholar at University of Pittsburgh.
  
• Research visit, Cincinnati.
  
• Workshop on New Connections Between Differential and Random Turn Games, PDE's and Image Processing, Vancouver, 27.7.-31.7.2009.
  
• Research visit, Lexington.
  
• AMS Sectional Meeting, Urbana-Champaign, 3.-5.8.2009.
• Function spaces, Differential Operators and Nonlinear Analysis, Helsinki, 25.-29.8.2008
  
• Spring school in harmonic analysis and PDE, Espoo, 2.-6.6.2008
  
• Research visit, Linköping, 13.-25.4.2008
  
• Finnish Mathematical Days, Espoo, 3.1.-4.1.2008
  
• Finland-Japan Joint Seminar on Analysis, Helsinki, 27-29.8.2007
  
• Lars Ahlfors Centennial Celebration, Helsinki, 20.-24.8.2007
  
• Qualitative Properties of Solutions to Elliptic and Parabolic Equations, Saariselkä, 7.-10.6.2007
  
• Research visit, Trondheim, 13.-27.5.2007
  
• ICM Satellites, Sevilla, Naples, 14.8-4.9.2006
  
• ICM 2006, Madrid, 22.-30.8.2006
  
• Global and Geometric Aspects of Nonlinear Partial Differential Equations, Evolène, 2.-8.7.2006
  
• Quasiweekend, Helsinki, 2.-3.12.2005
  
• Nonlinear parabolic problems, Espoo , 17.-21.10.2005
  
• The 15th Jyväskylä summer school, Jyväskylä, 15-19.8.2005
  
• Classics in PDE, Stockholm, 1-4.6.2005
  
• The p-Laplace equation, the infinity-Laplace equation and related topics, Linköping, 14 - 16.10.2004
  
• HARNACK INEQUALITIES and POSITIVITY for SOLUTIONS of PARTIAL DIFFERENTIAL EQUATIONS, Cortona, 12 - 18.6.2005
  
• Trends in the Calculus of Variations, Parma, 15 - 18.9.2004