Mikko Parviainen
Associate professor at University of Jyväskylä.
Docent of Mathematics
Contact information
Research interests
- nonlinear partial differential
equations (parabolic, in particular), stochastic game theory, calculus of variations, nonlinear potential
theory.
Conferences and minicourses
- Workshop on stochastic analysis and nonlinear partial differential equations at the Department of Mathematics and Statistics, University of Jyväskylä, on 11.-12.6.2020.
- Jyväskylä summer school at University of Jyväskylä, Finland, on 6.-17.8.2018. Application DL for students outside JyU April 30.
- Nonlinear, nonlocal problems and stochastic methods at Aalto University, Finland, on 7.-9.12.2016.
- Nonlinear PDEs and stochastic methods at the Department of Mathematics and Statistics, University of Jyväskylä, on 10.-13.06.2014.
- Workshop on Stochastics, Harmonic Analysis and PDEs at the Department of Mathematics and Statistics, University of Jyväskylä, on 19.12.-20.12.2013.
Research team in 'Stochastic games and nonlinear partial differential equations'
Teaching and advising
Lecture notes
Here are some of my lecture notes, more can be found through the course web sites.
Research papers
- Hölder regularity for stochastic processes with bounded and measurable increments (with Á. Arroyo and P. Blanc).
- Gradient and Lipschitz estimates for tug-of-war type games (with A. Attouchi and H. Luiro) SIAM J. Math. Anal 53(2): 1295-1319, 2021. Preprint in arXiv.
- Asymptotic Hölder Regularity for Ellipsoid Process (with Á. Arroyo) ESAIM Control Optim. Calc. Var. 26: Paper No. 112, pages 31, 2020. Preprint in arXiv.
- Convergence of dynamic programming principles for the p-Laplacian (with F. del Teso, J. J. Manfredi) To appear in Adv. Calc. Var. Preprint in arXiv.
- Equivalence between radial solutions of different parabolic gradient-diffusion equations and applications (with J. L. Vázquez) Ann. Sc. Norm. Super. Pisa Cl. Sci. 21:303-359, 2020. Preprint in arXiv.
- Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities (with Á. Arroyo, H. Luiro, and E. Ruosteenoja) Potential Anal. 53(2):565-589, 2020. Preprint in arXiv.
- A remark on infinite initial values for quasilinear parabolic equations (with P. Lindqvist) Nonlinear Anal. 194:111391, 2020. Preprint in arXiv.
- The tusk condition and Petrovski criterion for the
normalized p-parabolic equation (with A. and J. Björn) J. Lond. Math. Soc. 100 (2):623-643, 2019. Preprint in arXiv.
- Supercaloric functions for the porous medium equation (with J. Kinnunen, P. Lehtelä, and P. Lindqvist) J. Evol. Equ. 19 (1):249-270, 2019. Preprint in arXiv.
- Regularity for nonlinear stochastic games (with H. Luiro). Ann. Inst. H. Poincaré Anal. Non Linéaire. 35 (6):1435-1456, 2018. Preprint in arXiv.
- Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian (with A. Attouchi) Commun. Contemp. Math. 20 (4):1750035, 2018. Preprint in arXiv.
- Tug-of-war games with varying probabilities and the normalized p(x)-Laplacian
(with Á. Arroyo and J. Heino) Commun. Pure Appl. Anal. 16 (3):915-944, 2017.
Preprint in arXiv.
- Gradient walk and p-harmonic functions (with H. Luiro) Proc. Amer. Math. Soc. 145: 4313-4324, 2017. Preprint in arXiv.
- C^{1,a} regularity for the normalized p-Poisson problem (with A. Attouchi and E. Ruosteenoja) J. Math. Pures Appl. 108 (4): 553-591, 2017. Preprint in arXiv.
- Tug-of-war, market manipulation and option pricing (with K. Nyström). Math. Finance 27 (2), 279-312, 2017.
Preprint in arXiv.
- Local regularity for time-dependent tug-of-war games with varying probabilities (with E. Ruosteenoja) J.
Differential
Equations 261(2): 1357-1398,
2016. Preprint in arXiv.
- Discontinuous gradient constraints and the infinity
Laplacian (with P. Juutinen and J.D. Rossi). Int. Math. Res. Not. IMRN 8: 2451-2492, 2016. Preprint in arXiv.
- Shadows of infinities (with T. Kuusi and P. Lindqvist). Ann. Mat. Pura Appl. 195(4): 1185-1206, 2016. Preprint in arXiv.
- Stability of degenerate parabolic Cauchy problems (with T. Lukkari). Commun. Pure Appl. Anal. 14(1): 201-216, 2015. Preprint in arXiv.
- Boundary regularity for degenerate and singular parabolic equations (with A. Björn, J. Björn, and U. Gianazza). Calc. Var. Partial Differential Equations. 52(3): 797-827, 2015.
Preprint in arXiv.
- Variational parabolic capacity (with B. Avelin and T. Kuusi). Discrete Contin. Dyn. Syst.35(12):5665-5688,
2015. Preprint pdf.
- Global higher integrability for parabolic quasiminimizers in metric spaces (with M. Masson). Journal d'Analyse Mathematique 126(1):307-339, 2015. Preprint in arXiv.
- On the existence and uniqueness of p-harmonious functions (with H. Luiro and E. Saksman). Differential and Integral Equations 27(3/4):201-216, 2014. Preprint in arXiv.
- Harnack's inequality for p-harmonic functions via stochastic games (with H. Luiro and E. Saksman). Comm. Partial Differential Equations 38(12):1985-2003, 2013. Preprint in arXiv.
- Local higher integrability for parabolic quasiminimizers in metric spaces (with M. Masson, M. Miranda Jr, and F. Paronetto). Ricerche Mat. 62(2):279-305, 2013. Preprint in arXiv.
- Local approximation of superharmonic and superparabolic functions in nonlinear potential theory (with J. Kinnunen and T. Lukkari). J. Fixed Point Theory Appl. 13(1):291-307, 2013. Preprint pdf.
- Nonlinear parabolic capacity
and polar sets of superparabolic functions
(with J. Kinnunen, R. Korte and T. Kuusi). Math. Ann. 355(4):1349-1381, 2013.
Preprint pdf .
- Solutions of nonlinear PDEs in the sense of averages
(with B. Kawohl and J.J. Manfredi). J. Math. Pures Appl. 97(2):173-188, 2012. Preprint pdf
.
- Irregular time dependent obstacles
(with P. Lindqvist). J. Funct. Anal. 263 (8):2458-2482, 2012. Preprint in arXiv.
- Nonhomogeneous variational problems and quasi-minimizers on metric spaces
(with J. Gong and J.J. Manfredi).
Manuscripta Math. 137(1):247-271, 2012.
Preprint in arXiv.
- Dynamic programming principle for tug-of-war games with noise
(with J.J. Manfredi and J.D. Rossi).
ESAIM Control Optim. Calc. Var. 18:81-90, 2012.
Preprint pdf.
- On the definition and properties of p-harmonious functions
(with J.J. Manfredi and J.D. Rossi).
Ann. Sc. Norm. Super. Pisa Cl. Sci. 11(2):215-241, 2012.
Preprint pdf.
- 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.
- 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.
- An existence result for superparabolic functions (with J.
Kinnunen and T. Lukkari), J. Funct. Anal. 258:713-728, 2010.
Preprint pdf.
- 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.
- Stability for degenerate parabolic equations (with J. Kinnunen), Adv. Calc. Var. 3(1):29-48, 2010.
Preprint pdf.
- 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.
- 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.
- 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
- Existence for a degenerate Cauchy problem (with T. Kuusi), Manuscripta Math. 128(2):213-249, 2009.
Preprint pdf.
- Nonlinear balayage on
metric spaces (with A. Björn, J. Björn, and T. Mäkäläinen), Nonlinear Anal. 71(5-6):2153-2171, 2009. Preprint
pdf.
- Reverse Hölder inequalities for singular parabolic equations near the boundary,
J.
Differential
Equations 246:512-540, 2009.
Preprint
pdf.
- Global gradient estimates for degenerate parabolic equations in
nonsmooth domains,
Ann. Mat. Pura Appl. 188(2):333-358,
2009. Preprint pdf.
- 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.
- Global higher
integrability for parabolic quasiminimizers in nonsmooth
domains,
Calc. Var. Partial Differential Equations
31(1):75-98, 2008.
Other:
- Peliteoria on päätöksenteon tiedettä, jota sovelletaan niin biologiassa kuin ydinasestrategioissa, Tiedeykkönen, Yle,
2/2019.
- Väitöstutkimuksia epälineaarisista parabolisista yhtälöistä ja
systeemeistä (with T. Kuusi), Arkhimedes,
1/2008. pdf.
- Global higher integrability for nonlinear parabolic partial differential equations in nonsmooth domains, Dissertation, Helsinki University of Technology,
Institute of Mathematics, 2007. pdf.
Research
groups