Department of Mathematics and Systems Analysis

Research groups

Recent publications of the NPDE group


  • J. Kinnunen, A. Nastasi and C. Pacchiano Camacho, Gradient higher intergrability for double phase problems on metric measure spaces (2023). Preprint (PDF)
  • W. Kim, J. Kinnunen and L. Särkiö, Lipschitz truncation method for the parabolic double-phase systems with applications (2023). Preprint (PDF)
  • 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 (2023). Preprint (PDF)
  • A. Aghajani and J. Kinnunen, Supersolutions to nonatonomous Choquard equations in general domains (2023).
  • 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)


  • J. Kinnunen, K. Myyryläinen, D. Yang and C. Zhu, Parabolic Muckenhoupt weights on spaces of homogeneous type. Preprint (PDF)
  • W. Kim, J. Kinnunen and K. Moring, Gradient higher integrability for degenerate parabolic double-phase systems. Preprint (PDF)
  • 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). Preprint (PDF)
  • J. Weigt, Endpoint Sobolev bounds for the uncentered fractional maximal function, Math. Z. 301 (2022), 2317-2337. Preprint (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, 5393-5423. Preprint (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, 2269-2290. DOI 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)
  • V. Buffa, M. Collins and C. Pacchiano Camacho, Existense of parabolic minimizers to the total variation flow on metric measure spaces. Manuscripta Math. (2022). 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)
  • 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. (to appear). 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), 3407-3416. Preprint (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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