Department of Mathematics and Systems Analysis

Research groups

Recent publications of the NPDE group


  • R. Gibara, R. Korte and N. Shanmugalingam, Solving a Dirichlet problem for unbounded domains via a conformal transformation. 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)
  • C. Pacchiano Camacho and A. Nastasi, Higher integrability and stability of (p,q)-quasiminimizers. Preprint (PDF)
  • L. Capogna, J. Kline, R. Korte, N. Shanmugalingam, Neumann problems for p-harmonic functions, and induced nonlocal operators in metric measure spaces. 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)
  • T. Takala, Nontrivial examples of JNp and VJNp functions, Math. Z. 302 (2022), 1279-1305. 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)
  • R. Korte and R. Gibara, Accessible parts of the boundary for domains in metric measure spaces, Ann. Fenn. Math. 47 (2022), no. 2, 695-706. 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)
  • S. Eriksson-Bique, G. Giovannardi, R. Korte, N. Shanmugalingam and G. Speight, Regularity of solutions to the fractional Cheeger-Laplacian on domains in metric spaces of bounded geometry. J. Differential Equations 306 (2022) 590-632. 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, Weak Harnack inequality for a mixed local and nonlocal parabolic equation. 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)
  • J. Kinnunen and K. Myyryläinen, Dyadic John-Nirenberg space. Proc. Roy. Soc. Edinburgh Sect. A. (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)
  • E. Durand-Cartagena, S. Eriksson-Bique and R. Korte, Equivalence of the BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality, Adv. Calc. Var. 14 (2021), 231-245. Preprint (PDF)
  • D. Azagra and C. Mudarra, C^{1,w} extension formulas for 1-jets on Hilbert spaces, Adv. Math. 389 (2021), Paper No. 107928, 44 pp. 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)


  • J. Weigt, Variation of the dyadic maximal function, Int. Math. Res. Not. IMRN (to appear). 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. (to appear). Preprint (PDF)
  • V. Vespri and M. Vestberg, An extensive study of the regularity properties of solutions to doubly singular equation, Adv. Calc. Var. (to appear). Preprint (PDF)
  • V. Bögelein, F. Duzaar, J. Kinnunen and C. Scheven, Higher integrability for doubly nonlinear parabolic systems, J. Math. Pures Appl. (9) 143 (2020), 31-72. Preprint (PDF)
  • K. Moring, C. Scheven, S. Schwarzacher and T. Singer, Global higher integrability of weak solutions of porous medium systems, Comm. Pure Appl. Anal. 19 (2020), 1697-1745. Preprint (PDF)
  • J. Ramos, O. Saari and J. Weigt, Weak diffrentiability for fractional maximal functions of general Lp functions on domains, Adv. Math. 368 (2020), 25 pp. Preprint (PDF)
  • J. Weigt, Almost-othogonality of restricted Haar functions. Proc. Amer. Math. Soc. 148 (2020), no. 2, 601-609.


  • T. Singer and M. Vestberg, Local Hölder continuity of weak solutions to a diffusive shallow water equation, Nonlinear Anal. 185 (2019), 306-335. 
  • T. Singer and M. Vestberg, Local boundedness of weak solutions to the diffusive wave approximation of the shallow water equations, J. Differential Equations 226 (2019), 3014-3033Preprint (PDF)
  • J. Kinnunen, R. Korte, J. Lehrbäck and A. Vähäkangas, A maximal function approach to two-measure Poincare inequalities, J. Geom. Anal. 29 (2019), 1763-1810. Preprint (PDF)
  • J. Kinnunen, J. L. Lehrbäck, A. Vähäkangas and X. Zhong, Maximal function estimates and self-improving results for Poincare inequalities, Manuscripta Math.158 (2019), 119-147. Preprint (PDF)
  • J. Kinnunen, P. Lehtelä, P. Lindqvist and M. Parviainen, Supercaloric functions for the porous medium equation, J. Evol. Equ. 19 (2019), 249-270. Preprint (PDF)
  • R. Korte, P. Lahti, X. Li and N. Shanmugalingam, Notions of Dirichlet problem for functions of least gradient in metric measure spaces, Rev. Mat. Iberoamericana 35 (2019), 1603-1648. Preprint (PDF)
  • R. Korte, P. Lehtelä and S. Sturm, Lower semicontinuous obstacles for the porous medium equation, J. Differential Equations 266 (2019), 1851-1864. Preprint (PDF)
  • V. Bögelein, F. Duzaar, R. Korte and C. Scheven, The higher integrability of weak solutions of porous medium systems, Adv. Nonlinear Anal. 8 (2019), 1004-1034. Preprint (PDF)

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

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