Department of Mathematics and Systems Analysis

Research groups

Recent publications of the NPDE group


  • E. Hausenblas and J. M. Tölle, The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem, (2023), Preprint (PDF)
  • F. Seib, W. Stannat and J. M. Tölle, Stability and moment estimates for the stochastic singular Φ-Laplace equation, J. Differential Equations (to appear), (2023), Author accepted manuscript (PDF)
  • D. Blömker and J.M. Tölle, Singular limits for stochastic equations, Stochastics and Dynamics, (2023), Author accepted manuscript (PDF)
  • M. Hinz, L. Viitasaari and J. M. Tölle, Variability of paths and differential equations with BV-coefficients, Annales de l'Institut Henri Poincaré B, Probabilités et Statistiques (to appear) (2023), Author accepted manuscript (PDF)
  • W. Kim, J. Kinnunen and L. Särkiö, Lipschitz truncation method for parabolic double-phase systems with applications (2023). Preprint (PDF)
  • A. Aghajani and J. Kinnunen, Supersolutions to nonatonomous Choquard equations in general domains (2023).
  • P. Garain, J. Kinnunen and W. Kim, on the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems, Forum Math. (to appear). Preprint (PDF)
  • J. Kinnunen, A. Nastasi and C. Pacchiano Camacho, Gradient higher intergrability for double phase problems on metric measure spaces, Proc. Amer. Math. Soc. (to appear). Preprint (PDF)
  • J. Kinnunen, K. Myyryläinen, D. Yang and C. Zhu, Paraboliv Muckenhoupt weight with time lag on spacees of homogeneous type with monotone geodesic property, Potential Anal. (2023). DOI 10.1007/s11118-023-10098-1. Preprint (PDF)
  • W. Kim, J. Kinnunen and K. Moring, Gradient higher integrability for degenerate parabolic double-phase systems, Arch. Ration. Mech. Anal. 247 (2023) no. 5, 79. DOI 10.1007/s00205-023-01918-0. Preprint (PDF)
  • A. Banerjee, P. Garain and J. Kinnunen, Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic p-Laplace equations. Commun. Contemp. Math. 25 (2023), no. 8, Paper No. 2250032, 23 pp. Preprint (PDF)
  • V. Buffa, M. Collins and C. Pacchiano Camacho, Existence of parabolic minimizers to the total variation flow on metric measure spaces, Manuscripta Math. 170 (2023), 109-145. Preprint (PDF)
  • P. Garain and J. Kinnunen, Weak Harnack inequality for a mixed local and nonlocal parabolic equation. J. Differential Equations 360 (2023), 373-406. Preprint (PDF)
  • J. Kinnunen and K. Myyryläinen, Dyadic John-Nirenberg space, Proc. Roy. Soc. Edinburgh Sect. A 153 (2023), 1-18. Preprint (PDF) 
  • C. Pacchiano Camacho and A. Nastasi, Higher integrability and stability of (p,q)-quasiminimizers, J. Differential Equations 324 (2023), 121-149. Preprint (PDF)


  • M. Hinz, L. Viitasaari and J. M. Tölle, Sobolev regularity of occupation measures and paths, variablity and compositions, Electronic J. Probability 27 (2022), no. 73, 1–29, DOI: 10.1214/22-EJP797.
  • V. Vespri and M. Vestberg, An extensive study of the regularity properties of solutions to doubly singular equation, Adv. Calc. Var. 15 (2022), no.3, 435-473. Preprint (PDF)
  • J. Kinnunen, K. Myyryläinen and D. Yang, John-Nirenberg inequalities for parabolic BMO, Math. Ann. (2022) DOI 10.1007/s00208-022-02480-y. Preprint (PDF)
  • J. Weigt, Endpoint Sobolev bounds for the uncentered fractional maximal function, Math. Z. 301 (2022), 2317-2337Preprint (PDF)
  • P. Garain and J. Kinnunen, On the regularity theory for mixed local and nonlocal quasilinear elliptic equations, Trans. Amer. Math. Soc. 375 (2022), no. 8, 5393-5423Preprint (PDF)
  • A. Banerjee, P. Garain and J. Kinnunen, Some local properties of subsolutions and supersolutions for a doubly nonlinear nonlocal parabolic p-Laplace equation, Ann. Mat. Pura Appl. (4) 201 (2022), no. 4, 1717-1751. Preprint (PDF)
  • J. Weigt, Variation of the uncenteted maximal characteristic function. Rev. Mat. Iberoam. 38 (2022), no. 3. 823-849. Preprint (PDF)
  • V. Buffa, J. Kinnunen and C. Pacchiano Camacho, Variational solutions to the total variation flow on metric measure spaces. Nonlinear Anal. 220 (2022), Paper No. 112859. Preprint (PDF)
  • J. Kinnunen, E.-K. Kurki and C. Mudarra, Characterizations of weak reverse Hölder inequalities on metric measure spaces, Math. Z. 301 (2022), no. 3, 2269-2290DOI 10.1007/s00209-022-02976-y.
  • K. Myyryläinen, Median-type John-Nirenberg space in metric measure spaces, J. Geom. Anal. 32 (2022), no. 4, 131. Preprint (PDF)
  • J. Kinnunen and C. Scheven, On the defintion of solution to the total variation flow, Calc. Var. Partial Differential Equations 61 (2022), no.1, Paper No. 40. Preprint (PDF)
  • E.-K. Kurki and C. Mudarra, On the  extension of Muckenhoupt weights in metric spaces. Nonlinear Anal. 215 (2022), Paper No. 112671. Preprint (PDF)
  • K. Moring and R. Rainer, Stability for systems of porous medium type. J. Math. Anal. Appl. 506 (2022), no. 1, Paper No. 125532. Preprint (PDF)


  • J. Weigt, The variation of the uncentered maximal operator with respect to cubes. Preprint (PDF)
  • C. Bilz and J. Weigt, The one-dimensional centred maximal function diminished the variation of indicator functions. Preprint (PDF)
  • P. Garain and J. Kinnunen, On the regularity theory for mixed local and nonlocal quasilinear parabolic equations. Ann. Sc. Norm. Super. Pisa Cl. Sci (5) (to apper). Preprint (PDF)
  • D. Beltran, C. González-Riquelme, J. Madrid and J. Weigt, Continuity of the gradient of the fractional maximal operator on W1,1(Rd), Math. Res. Lett. (to appear). Preprint (PDF)
  • A. Nastasi and C. Pacchiano Camacho, Regularity properties of quasiminimizers of a (p,q)-Dirichlet integral, Calc. Var. Partial Differential Equations 60 (2021), Paper No. 227. Preprint (PDF)
  • J. Kinnunen, J. Lehrbäck and A. Vähäkangas, Maximal function methods for Sobolev spaces. Mathematical Surverys and Monographs, 257. American Mathematical Society, 2021, 338 pp.
  • E.-K. Kurki and A. Vähäkangas, Weighted norm inequalities in a bounded domain by the sparse domination method, Rev. Mat. Complut. 34 (2021), 435-467. Preprint (PDF)
  • P. Garain and J. Kinnunen, Nonexistence of variational minimizers related to a quasilinear singular problem in metric measure spaces, Proc. Amer. Math. Soc. 149 (2021), 3407-3416Preprint (PDF)
  • V. Bögelein, N. Dietrich and M. Vestberg, Existence of solutions to a diffusive shallow medium equation, J. Evol. Equ. 21 (2021), 845-889. Preprint (PDF)
  • R. Kr. Giri, J. Kinnunen and K. Moring, Supercaloric functions for the parabolic p-Laplace equation in the fast diffusion case. NoDEA Nonlinear Differential Equations Appl. 28 (2021), no. 3, Paper No. 33. Preprint (PDF)

Many more publications can be found on the individual websites of the group members

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