Mikko Parviainen
University lecturer 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
- 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
Research papers
- Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities (with Á. Arroyo, H. Luiro, and E. Ruosteenoja) Preprint in arXiv.
- Equivalence between radial solutions of different parabolic gradient-diffusion equations and applications (with J. L. Vázquez) Preprint in arXiv.
- Supercaloric functions for the porous medium equation (with J. Kinnunen, P. Lehtelä, and P. Lindqvist) Preprint in arXiv.
- The tusk condition and Petrovski criterion for the
normalized p-parabolic equation (with A. and J. Björn) Preprint in arXiv.
- Regularity for nonlinear stochastic games (with H. Luiro) To appear in Ann. Inst. H. Poincaré Anal. Non Linéaire. Preprint in arXiv.
- Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian (with A. Attouchi) To appear in Commun. Contemp. Math. 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:
- 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