Publications

Preprints

• V. Bögelein, F. Duzaar, U. Gianazza, N. Liao, and C. Scheven. Hölder Continuity of the Gradient of Solutions to Doubly Non-Linear Parabolic Equations. arXiv:2305.08539

• V. Bögelein, F. Duzaar, and G. Treu. Parabolic PDEs with Dynamic Data under a Bounded Slope Condition. arXiv:2504.17556

Research papers

1. V. Bögelein, F. Duzaar, U. Gianazza, N. Liao, and C. Scheven. Intrinsic Harnack estimates for singular doubly non-linear equations. Calc. Var. Partial Differential Equations, to appear.  

2. G. Akagi, V. Bögelein, A. Marveggio, U. Stefanelli. Weighted Inertia-Dissipation-Energy approach to doubly nonlinear wave equations.  J. Funct. Anal. 289 (2025) no. 8, Paper No. 111067.

3. V. Bögelein, F. Duzaar, U. Gianazza, and N. Liao. Local boundedness and higher integrability for the sub-critical singular porous medium system. Math. Ann. 392 (2025), no. 3, 3161–3245.

4. V. Bögelein, F. Duzaar, N. Liao, G. Molica-Bisci, and R. Servadei. Regularity for the fractional p-Laplace equation. J. Funct. Anal.  289 (2025), no. 9, Paper No. 111078. 

5. V. Bögelein, F. Duzaar, N. Liao, G. Molica-Bisci, and R. Servadei. Gradient regularity for (s,p)-harmonic functions. Calc. Var. Partial Differential Equations 64 (2025), no. 8, Paper No. 253, 63 pp.

6. V. Bögelein, F. Duzaar, N. Liao, and K. Moring. Gradient estimates for the fractional p-Poisson equation. J. Math. Pures Appl. (9) 204 (2025), Paper No. 103764, 25 pp.

7. V. Bögelein, F. Duzaar, R. Giova, and A. Passarelli di Napoli. Gradient regularity for a class of widely degenerate parabolic systems. SIAM J. Math. Anal. 56 (2024), no.4, 5017–5078.

8. V Bögelein and M. Strunk. A comparison principle for doubly nonlinear parabolic partial differential equations. Ann. Mat. Pura Appl. (4) 203 (2024), no. 2, 779–804.

9. V. Bögelein, F. Duzaar, R. Giova, and A. Passarelli di Napoli. Higher regularity in congested traffic dynamics. Math. Ann. 385 (2023), no. 3-4, 1823–1878.

10. V. Bögelein, F. Duzaar, N. Liao, and L. Schätzler. On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II. Rev. Mat. Iberoam. 39 (2023), no. 3, 1005–1037.

11. V. Bögelein, F. Duzaar, N. Liao, and C. Scheven. Boundary regularity for parabolic systems in convex domains. J. Lond. Math. Soc. (2) 105 (2022), no. 3, 1702–1751.

12. V. Bögelein, F. Duzaar, N. Liao, and C. Scheven. Gradient Hölder regularity for degenerate parabolic systems. Nonlinear Anal. 225 (2022), Paper No. 113119, 61 pp.

13. V. Bögelein, F. Duzaar, P. Marcellini, and C. Scheven. Boundary regularity for elliptic systems with  p,q -growth. J. Math. Pures Appl. (9) 159 (2022), 250–293.

14. V. Bögelein, F. Duzaar,  and C. Scheven. Higher integrability for doubly nonlinear parabolic systems. Partial Differ. Equ. Appl. 3 (2022), no. 6, Paper No. 74, 41 pp.

15. V. Bögelein, N. Dietrich, and M. Vestberg. Existence of solutions to a diffusive shallow medium equation. J. Evol. Equ. 21 (2021), no. 1, 845–889. Corrigendum.

16. V. Bögelein, F. Duzaar, and N. Liao. On the Hölder regularity of signed solutions to a doubly nonlinear equation. J. Funct. Anal. 281 (2021), no. 9, Paper No. 109173, 58 pp.

17. V. Bögelein, A. Heran, L. Schätzler, and T. Singer. Harnack's inequality for doubly nonlinear equations of slow diffusion type. Calc. Var. Partial Differential Equations 60 (2021), no. 6, Paper No. 215, 35 pp.

18. V. Bögelein, B. Dacorogna, F. Duzaar, P. Marcellini, and C. Scheven. Integral convexity and parabolic systems. SIAM J. Math. Anal. 52 (2020), no. 2, 1489–1525.

19. 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.

20. V. Bögelein, F. Duzaar, and C. Scheven. Higher integrability for the singular porous medium system. J. Reine Angew. Math. 767 (2020), 203–230.

21. V. Bögelein and T. Stanin. The one-sided bounded slope condition in evolution problems. Ann. Mat. Pura Appl. (4) 199 (2020), no. 2, 573–587.

22. V. Bögelein, F. Duzaar, R. Korte, and . Scheven. The higher integrability of weak solutions of porous medium systems. Adv. Nonlinear Anal. 8 (2019), no. 1, 1004–1034.

23. V. Bögelein, F. Duzaar, L. Schätzler, and C. Scheven. Existence for evolutionary problems with linear growth by stability methods. J. Differential Equations 266 (2019), no. 11, 7709–7748.

24. V. Bögelein, P. Lehtelä, and S. Sturm. Regularity of weak solutions and supersolutions to the porous medium equation. Nonlinear Anal. 185 (2019), 49–67.

25. V. Bögelein, F. Duzaar, P. Marcellini, and C. Scheven. A variational approach to doubly nonlinear equations. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 29 (2018), no. 4, 739–772.

26. V. Bögelein, F. Duzaar, P. Marcellini, and C. Scheven. Doubly nonlinear equations of porous medium type. Arch. Ration. Mech. Anal. 229 (2018), no. 2, 503–545.

27. V. Bögelein, F. Duzaar, C. Scheven, and T. Singer. Existence of variational solutions in noncylindrical domains. SIAM J. Math. Anal. 50 (2018), no. 3, 3007–3057.

28. V. Bögelein, F. Duzaar, and N. Fusco. A quantitative isoperimetric inequality on the sphere. Adv. Calc. Var. 10 (2017), no. 3, 223–265.

29. V. Bögelein, F. Duzaar, P. Marcellini, and Stefano Signoriello. Parabolic equations and the bounded slope condition. Ann. Inst. H. Poincaré C Anal. Non Linéaire 34 (2017), no. 2, 355–379.

30. V. Bögelein, F. Duzaar, and C. Scheven. The obstacle problem for parabolic minimizers. J. Evol. Equ. 17 (2017), no. 4, 1273–1310.

31. V. Bögelein, T. Lukkari, and C. Scheven. Hölder regularity for degenerate parabolic obstacle problems. Ark. Mat. 55 (2017), no. 1, 1–39.

32. V. Bögelein, F. Ragnedda, S. Vernier Piro, and V. Vespri. Moser-Nash kernel estimates for degenerate parabolic equations. J. Funct. Anal. 272 (2017), no. 7, 2956–2986. 

33. V. Bögelein, F. Duzaar, and U. Gianazza. Sharp boundedness and continuity results for the singular porous medium equation. Israel J. Math. 214 (2016), no. 1, 259–314.

34. V. Bögelein, F. Duzaar, and C. Scheven. The obstacle problem for the total variation flow. Ann. Sci. Éc. Norm. Supér. (4) 49 (2016), no. 5, 1143–1188.

35. V. Bögelein, F. Duzaar, and C. Scheven. The total variation flow with time dependent boundary values. Calc. Var. Partial Differential Equations 55 (2016), no. 4, Art. 108, 31 pp.

36. V. Bögelein. Global gradient bounds for the parabolic p-Laplacian system. Proc. Lond. Math. Soc. (3) 111 (2015), no. 3, 633–680.

37. V. Bögelein. Partial boundary regularity of non-linear parabolic systems in low dimensions. Analysis (Berlin) 35 (2015), no. 1, 1–28.

38. V. Bögelein, F. Duzaar, and N. Fusco. A sharp quantitative isoperimetric inequality in higher codimension. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 26 (2015), no. 3, 309–362.

39. V. Bögelein, F. Duzaar, and U. Gianazza. Very weak solutions of singular porous medium equations with measure data. Commun. Pure Appl. Anal. 14 (2015), no. 1, 23–49.

40. V. Bögelein, F. Duzaar, and P. Marcellini. A time dependent variational approach to image restoration. SIAM J. Imaging Sci. 8 (2015), no. 2, 968–1006.

41. V. Bögelein, F. Duzaar, P. Marcellini, and Stefano Signoriello. Nonlocal diffusion equations. J. Math. Anal. Appl. 432 (2015), no. 1, 398–428.

42. V. Bögelein, F. Duzaar, and C. Scheven. A sharp quantitative isoperimetric inequality in hyperbolic  n-space. Calc. Var. Partial Differential Equations 54 (2015), no. 4, 3967–4017.

43. V. Bögelein, F. Duzaar,  and C. Scheven. Short-time regularity for the  H-surface flow. Int. Math. Res. Not. IMRN (2015), no. 12, 3694–3750.

44. V. Bögelein, T. Lukkari, and C. Scheven. The obstacle problem for the porous medium equation. Math. Ann. 363 (2015), no. 1-2, 455–499.

45. P. Baroni and V. Bögelein. Calderón-Zygmund estimates for parabolic p(x,t)-Laplacian systems. Rev. Mat. Iberoam. 30 (2014), no. 4, 1355–1386.

46. V. Bögelein. Global Calderón-Zygmund theory for nonlinear parabolic systems. Calc. Var. Partial Differential Equations 51 (2014), no. 3-4, 555–596.

47. V. Bögelein, F. Duzaar, and U. Gianazza. Continuity estimates for porous medium type equations with measure data. J. Funct. Anal. 267 (2014), no. 9, 3351–3396.

48. V. Bögelein and Q. Li. Very weak solutions of degenerate parabolic systems with non-standard p(x,t)-growth. Nonlinear Anal. 98 (2014), 190–225.

49. V. Bögelein, F. Duzaar, and P. Marcellini. Existence of evolutionary variational solutions via the calculus of variations. J. Differential Equations 256 (2014), no. 12, 3912–3942.

50. V. Bögelein, F. Duzaar, and U. Gianazza. Porous medium type equations with measure data and potential estimates. SIAM J. Math. Anal. 45 (2013), no. 6, 3283–3330.

51. V. Bögelein, F. Duzaar, and P. Marcellini. Parabolic equations with  p,q-growth. J. Math. Pures Appl. (9) 100 (2013), no. 4, 535–563.

52. V. Bögelein, F. Duzaar, and P. Marcellini. Parabolic systems with  p,q-growth: a variational approach. Arch. Ration. Mech. Anal. 210 (2013), no. 1, 219–267.

53. V. Bögelein, F. Duzaar, and G. Mingione. The regularity of general parabolic systems with degenerate diffusion. Mem. Amer. Math. Soc. 221 (2013), no. 1041, vi+143 pp.

54. V. Bögelein, F. Duzaar, and C. Scheven. Weak solutions to the heat flow for surfaces of prescribed mean curvature. Trans. Amer. Math. Soc. 365 (2013), no. 9, 4633–4677.

55. V. Bögelein. Partial regularity for minimizers of discontinuous quasi-convex integrals with degeneracy. J. Differential Equations 252 (2012), no. 2, 1052–1100.

56. V. Bögelein and F. Duzaar. Hölder estimates for parabolic  p(x,t) -Laplacian systems. Math. Ann. 354 (2012), no. 3, 907–938.

57. V. Bögelein, F. Duzaar, J. Habermann, and C. Scheven. Stationary electro-rheological fluids: low order regularity for systems with discontinuous coefficients. Adv. Calc. Var. 5 (2012), no. 1, 1–57.

58. V. Bögelein, F. Duzaar, and C. Scheven. Global solutions to the heat flow for  m -harmonic maps and regularity. Indiana Univ. Math. J. 61 (2012), no. 6, 2157–2210.

59. V. Bögelein, M. Foss, and G. Mingione. Regularity in parabolic systems with continuous coefficients. Math. Z. 270 (2012), no. 3-4, 903–938.

60. V. Bögelein and C. Scheven. Higher integrability in parabolic obstacle problems. Forum Math. 24 (2012), no. 5, 931–972.

61. V. Bögelein and F. Duzaar. Higher integrability for parabolic systems with non-standard growth and degenerate diffusions. Publ. Mat. 55 (2011), no. 1, 201–250.

62. V. Bögelein, F. Duzaar, J. Habermann, and C. Scheven. Partial Hölder continuity for discontinuous elliptic problems with VMO-coefficients. Proc. Lond. Math. Soc. (3) 103 (2011), no. 3, 371–404.

63. V. Bögelein, F. Duzaar, and G. Mingione. Degenerate problems with irregular obstacles. J. Reine Angew. Math. 650 (2011), 107–160.

64. V. Bögelein, F. Duzaar, and G. Mingione. The boundary regularity of non-linear parabolic systems I. Ann. Inst. H. Poincaré C Anal. Non Linéaire 27 (2010), no. 1, 201–255.

65. V. Bögelein, F. Duzaar, and G. Mingione. The boundary regularity of non-linear parabolic systems II. Ann. Inst. H. Poincaré C Anal. Non Linéaire 27 (2010), no. 1, 145–200.

66. V. Bögelein and J. Habermann. Gradient estimates via non standard potentials and continuity. Ann. Acad. Sci. Fenn. Math. 35 (2010), no. 2, 641–678.

67. V. Bögelein and M. Parviainen. Self-improving property of nonlinear higher order parabolic systems near the boundary. NoDEA Nonlinear Differential Equations Appl. 17 (2010), no. 1, 21–54. 

68. V. Bögelein. Partial regularity and singular sets of solutions of higher order parabolic systems. Ann. Mat. Pura Appl. (4) 188 (2009), no. 1, 61–122.

69. Verena Bögelein. Very weak solutions of higher-order degenerate parabolic systems. Adv. Differential Equations 14 (2009), no. 1-2, 121–200.

70.  V. Bögelein. Higher integrability for weak solutions of higher order degenerate parabolic systems. Ann. Acad. Sci. Fenn. Math. 33 (2008), no. 2, 387–412.

71. V. Bögelein and A. Zatorska-Goldstein. Higher integrability of very weak solutions of systems of p(x)-Laplacean type. J. Math. Anal. Appl. 336 (2007), no. 1, 480–497. 

Survey papers, proceedings, research announcements, etc.

• V. Bögelein, F. Duzaar, N. Liao, G. Molica-Bisci, and R. Servadei. Higher regularity theory for (s,p)-harmonic functions. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 35 (2024), no. 2, 311–321.

• V. Bögelein, F. Duzaar, and C. Scheven. Evolutionary problems in non-cylindrical domains. Springer INdAM Ser. 46. Springer, Cham, 2021, 43–60.

• I. Agricola, V. Bögelein, and F. Duzaar.  In memoriam Thomas Friedrich (1949–2018). Ann. Global Anal. Geom. 56 (2019), no. 4, 613–630.

• V. Bögelein. A Variational Approach to Porous Medium Type Equations. IMN Internationale Mathematische Nachrichten (2017), 235:17-32.