Bögelein, Verena; Duzaar, Frank; Gianazza, Ugo; Liao, Naian; Scheven, Christoph. Intrinsic Harnack estimates for singular doubly non-linear equations. To appear in Calc. Var. Partial Differential Equations.

Bögelein, Verena; Duzaar, Frank; Liao, Naian; Bisci, Giovanni-Molica; Servadei, Raffaella. Gradient regularity for (s,p)-harmonic functions. Calc. Var. 64, 253 (2025). https://doi.org/10.1007/s00526-025-03116-0

Bögelein, Verena; Duzaar, Frank; Liao, Naian; Bisci, Giovanni-Molica; Servadei, Raffaella. Regularity for the fractional p-Laplace equation. J. Funct. Anal. (2025). https://doi.org/10.1016/j.jfa.2025.111078

Bögelein, Verena; Duzaar, Frank; Liao, Naian, Moring, Kristian. Gradient estimates for the p-Poission equation.  J. Math. Pures Appl. (2025). https://doi.org/10.1016/j.matpur.2025.103764

Bögelein, Verena; Duzaar, Frank; Gianazza, Ugo; Liao, Naian. Local boundedness and higher integrability for the sub-critical singular porous medium system. Math. Ann, (2025). https://doi.org/10.1007/s00208-025-03160-3

Bögelein, Verena; Duzaar, Frank; Giova, Raffaella; Passarelli di Napoli, Antonia. Gradient regularity for a class of widely degenerate parabolic systems. SIAM J. Math. Anal. 56 (2024), no.4, 5017–5078.

Bögelein, Verena; Duzaar, Frank; Liao, Naian; Schätzler, Leah. On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II. Rev. Mat. Iberoam. 39 (2023), no. 3, 1005–1037.

Bögelein, Verena; Duzaar, Frank; Giova, Raffaella; Passarelli di Napoli, Antonia. Higher regularity in congested traffic dynamics. Math. Ann. 385 (2023), no. 3-4, 1823–1878.

Bögelein, Verena; Duzaar, Frank; Scheven, Christoph. Higher integrability for doubly nonlinear parabolic systems. Partial Differ. Equ. Appl. 3 (2022), no. 6, Paper No. 74, 41 pp.

Bögelein, Verena; Duzaar, Frank; Liao, Naian; Scheven, Christoph. Gradient Hölder regularity for degenerate parabolic systems. Nonlinear Anal. 225 (2022), Paper No. 113119, 61 pp.

Bögelein, Verena; Duzaar, Frank; Liao, Naian; Scheven, Christoph. Boundary regularity for parabolic systems in convex domains. J. Lond. Math. Soc. (2) 105 (2022), no. 3, 1702–1751.

Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo; Scheven, Christoph. Boundary regularity for elliptic systems with  p,q -growth. J. Math. Pures Appl. (9) 159 (2022), 250–293.

Bögelein, Verena; Duzaar, Frank; Liao, Naian. On the Hölder regularity of signed solutions to a doubly nonlinear equation. J. Funct. Anal. 281 (2021), no. 9, Paper No. 109173, 58 pp.

Bögelein, Verena; Duzaar, Frank; Kinnunen, Juha; Scheven, Christoph.  Higher integrability for doubly nonlinear parabolic systems. J. Math. Pures Appl. (9) 143 (2020), 31–72.

Bögelein, Verena; Duzaar, Frank; Scheven, Christoph. Higher integrability for the singular porous medium system. J. Reine Angew. Math. 767 (2020), 203–230.

Bögelein, Verena; Dacorogna, Bernard; Duzaar, Frank; Marcellini, Paolo; Scheven, Christoph. Integral convexity and parabolic systems. SIAM J. Math. Anal. 52 (2020), no. 2, 1489–1525.

Bögelein, Verena; Duzaar, Frank; Schätzler, Leah; Scheven, Christoph. Existence for evolutionary problems with linear growth by stability methods. J. Differential Equations 266 (2019), no. 11, 7709–7748.

Bögelein, Verena; Duzaar, Frank; Korte, Riikka; Scheven, Christoph. The higher integrability of weak solutions of porous medium systems. Adv. Nonlinear Anal. 8 (2019), no. 1, 1004–1034.

Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo; Scheven, Christoph. A variational approach to doubly nonlinear equations. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 29 (2018), no. 4, 739–772.

Bögelein, Verena; Duzaar, Frank; Scheven, Christoph; Singer, Thomas. Existence of variational solutions in noncylindrical domains. SIAM J. Math. Anal. 50 (2018), no. 3, 3007–3057.

Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo; Scheven, Christoph. Doubly nonlinear equations of porous medium type. Arch. Ration. Mech. Anal. 229 (2018), no. 2, 503–545.

Bögelein, Verena; Duzaar, Frank; Scheven, Christoph. The obstacle problem for parabolic minimizers. J. Evol. Equ. 17 (2017), no. 4, 1273–1310.

Bögelein, Verena; Duzaar, Frank; Fusco, Nicola. A quantitative isoperimetric inequality on the sphere. Adv. Calc. Var. 10 (2017), no. 3, 223–265.

Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo; Signoriello, Stefano. Parabolic equations and the bounded slope condition. Ann. Inst. H. Poincaré C Anal. Non Linéaire 34 (2017), no. 2, 355–379.

Bögelein, Verena; Duzaar, Frank; Scheven, Christoph. The obstacle problem for the total variation flow. Ann. Sci. Éc. Norm. Supér. (4) 49 (2016), no. 5, 1143–1188.

Bögelein, Verena; Duzaar, Frank; Gianazza, Ugo. Sharp boundedness and continuity results for the singular porous medium equation. Israel J. Math. 214 (2016), no. 1, 259–314.

Bögelein, Verena; Duzaar, Frank; Scheven, Christoph. The total variation flow with time dependent boundary values. Calc. Var. Partial Differential Equations 55 (2016), no. 4, Art. 108, 31 pp.

Bögelein, Verena; Duzaar, Frank; Scheven, Christoph. A sharp quantitative isoperimetric inequality in hyperbolic  n-space. Calc. Var. Partial Differential Equations 54 (2015), no. 4, 3967–4017.

Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo; Signoriello, Stefano. Nonlocal diffusion equations. J. Math. Anal. Appl. 432 (2015), no. 1, 398–428.

Bögelein, Verena; Duzaar, Frank; Fusco, Nicola. A sharp quantitative isoperimetric inequality in higher codimension. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 26 (2015), no. 3, 309–362.

Bögelein, Verena; Duzaar, Frank; Scheven, Christoph. Short-time regularity for the  H -surface flow. Int. Math. Res. Not. IMRN(2015), no. 12, 3694–3750.

Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo. A time dependent variational approach to image restoration. SIAM J. Imaging Sci. 8 (2015), no. 2, 968–1006.

Duzaar, Frank; Scheven, Christoph. The evolution of  H -surfaces with a Plateau boundary condition. Ann. Inst. H. Poincaré C Anal. Non Linéaire 32 (2015), no. 1, 109–157.

Bögelein, Verena; Duzaar, Frank; Gianazza, Ugo. Very weak solutions of singular porous medium equations with measure data. Commun. Pure Appl. Anal. 14 (2015), no. 1, 23–49.

Bögelein, Verena; Duzaar, Frank; Gianazza, Ugo. Continuity estimates for porous medium type equations with measure data. J. Funct. Anal. 267 (2014), no. 9, 3351–3396.

 Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo. Existence of evolutionary variational solutions via the calculus of variations. J. Differential Equations 256 (2014), no. 12, 3912–3942.

Bögelein, Verena; Duzaar, Frank; Gianazza, Ugo. Porous medium type equations with measure data and potential estimates. SIAM J. Math. Anal. 45 (2013), no. 6, 3283–3330.

Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo. Parabolic equations with  p,q -growth. J. Math. Pures Appl. (9) 100 (2013), no. 4, 535–563.

Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo. Parabolic systems with  p,q -growth: a variational approach. Arch. Ration. Mech. Anal. 210 (2013), no. 1, 219–267.

Bögelein, Verena; Duzaar, Frank; Scheven, Christoph. Weak solutions to the heat flow for surfaces of prescribed mean curvature. Trans. Amer. Math. Soc. 365 (2013), no. 9, 4633–4677.

Bögelein, Verena; Duzaar, Frank; Mingione, Giuseppe. The regularity of general parabolic systems with degenerate diffusion. Mem. Amer. Math. Soc. 221 (2013), no. 1041, vi+143 pp.

Bögelein, Verena; Duzaar, Frank; Scheven, Christoph. Global solutions to the heat flow for  m -harmonic maps and regularity. Indiana Univ. Math. J. 61 (2012), no. 6, 2157–2210.

Bögelein, Verena; Duzaar, Frank. Hölder estimates for parabolic  p(x,t) -Laplacian systems. Math. Ann. 354 (2012), no. 3, 907–938.

Duzaar, Frank; Habermann, Jens. Partial regularity for parabolic systems with non-standard growth. J. Evol. Equ. 12 (2012), no. 1, 203–244.

Bögelein, Verena; Duzaar, Frank; Habermann, Jens; Scheven, Christoph. Stationary electro-rheological fluids: low order regularity for systems with discontinuous coefficients. Adv. Calc. Var. 5 (2012), no. 1, 1–57.

Duzaar, Frank; Mingione, Giuseppe; Steffen, Klaus. Parabolic systems with polynomial growth and regularity. Mem. Amer. Math. Soc. 214 (2011), no. 1005, x+118 pp.

Bögelein, Verena; Duzaar, Frank; Habermann, Jens; Scheven, Christoph. Partial Hölder continuity for discontinuous elliptic problems with VMO-coefficients. Proc. Lond. Math. Soc. (3) 103 (2011), no. 3, 371–404.

Duzaar, Frank; Mingione, Giuseppe. Gradient estimates via non-linear potentials. Amer. J. Math. 133 (2011), no. 4, 1093–1149.

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

Bögelein, Verena; Duzaar, Frank; Mingione, Giuseppe. Degenerate problems with irregular obstacles. J. Reine Angew. Math. 650 (2011), 107–160.

Duzaar, Frank; Mingione, Giuseppe. Local Lipschitz regularity for degenerate elliptic systems. Ann. Inst. H. Poincaré C Anal. Non Linéaire 27 (2010), no. 6, 1361–1396.

Duzaar, Frank; Mingione, Giuseppe. Gradient continuity estimates. Calc. Var. Partial Differential Equations 39 (2010), no. 3-4, 379–418.

Duzaar, Frank; Mingione, Giuseppe. Gradient estimates via linear and nonlinear potentials. J. Funct. Anal. 259 (2010), no. 11, 2961–2998.

Bögelein, Verena; Duzaar, Frank; Mingione, Giuseppe. The boundary regularity of non-linear parabolic systems I. Ann. Inst. H. Poincaré C Anal. Non Linéaire 27 (2010), no. 1, 201–255.

Bögelein, Verena; Duzaar, Frank; Mingione, Giuseppe. The boundary regularity of non-linear parabolic systems II. Ann. Inst. H. Poincaré C Anal. Non Linéaire 27 (2010), no. 1, 145–200.

Duzaar, Frank; Mingione, Giuseppe. Harmonic type approximation lemmas. J. Math. Anal. Appl. 352 (2009), no. 1, 301–335.

Duzaar, Frank; Kristensen, Jan; Mingione, Giuseppe. The existence of regular boundary points for non-linear elliptic systems. J. Reine Angew. Math. 602 (2007), 17–58.

Duzaar, Frank; Grotowski, Joseph F.; Kronz, Manfred. Regularity of almost minimizers of quasi-convex variational integrals with subquadratic growth. Ann. Mat. Pura Appl. (4) 184 (2005), no. 4, 421–448.

Duzaar, Frank; Mingione, Giuseppe. Second order parabolic systems, optimal regularity, and singular sets of solutions. Ann. Inst. H. Poincaré C Anal. Non Linéaire 22 (2005), no. 6, 705–751.

Duzaar, Frank; Grotowski, Joseph F.; Kronz, Manfred. Partial and full boundary regularity for minimizers of functionals with nonquadratic growth. J. Convex Anal. 11 (2004), no. 2, 437–476.

Duzaar, Frank; Gastel, Andreas; Mingione, Giuseppe. Elliptic systems, singular sets and Dini continuity. Comm. Partial Differential Equations 29 (2004), no. 7-8, 1215–1240.

Duzaar, Frank; Mingione, Giuseppe. Regularity for degenerate elliptic problems via  p-harmonic approximation. Ann. Inst. H. Poincaré C Anal. Non Linéaire 21 (2004), no. 5, 735–766.

Duzaar, Frank; Mingione, Giuseppe. The  p-harmonic approximation and the regularity of  p-harmonic maps. Calc. Var. Partial Differential Equations 20 (2004), no. 3, 235–256..

Duzaar, Frank; Kronz, Manfred. Regularity of  ω -minimizers of quasi-convex variational integrals with polynomial growth. Differential Geom. Appl. 17 (2002), no. 2-3, 139–152.

Duzaar, Frank; Steffen, Klaus. Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals. J. Reine Angew. Math. 546 (2002), 73–138.

Duzaar, Frank; Gastel, Andreas. Nonlinear elliptic systems with Dini continuous coefficients. Arch. Math. (Basel) 78 (2002), no. 1, 58–73.

Duzaar, Frank; Gastel, Andreas; Grotowski, Joseph F. Optimal partial regularity for nonlinear elliptic systems of higher order. J. Math. Sci. Univ. Tokyo 8 (2001), no. 3, 463–499.

Duzaar, Frank; Grotowski, Joseph F. Optimal interior partial regularity for nonlinear elliptic systems: the method of  A -harmonic approximation. Manuscripta Math. 103 (2000), no. 3, 267–298.

 Duzaar, Frank; Gastel, Andreas; Grotowski, Joseph F. Partial regularity for almost minimizers of quasi-convex integrals. SIAM J. Math. Anal. 32 (2000), no. 3, 665–687.

Duzaar, Frank; Grotowski, Joseph F. Existence and regularity for higher-dimensional  H -systems. Duke Math. J. 101 (2000), no. 3, 459–485.

Duzaar, Frank; Steffen, Klaus. Parametric surfaces of least  H -energy in a Riemannian manifold. Math. Ann. 314 (1999), no. 2, 197–244.

Duzaar, Frank; Gastel, Andreas. Minimizing  p -harmonic maps at a free boundary. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 1 (1998), no. 2, 391–405.

Duzaar, Frank; Kuwert, Ernst. Minimization of conformally invariant energies in homotopy classes. Calc. Var. Partial Differential Equations 6 (1998), no. 4, 285–313.

Duzaar, Frank. Boundary regularity for area minimizing currents with prescribed volume. J. Geom. Anal. 7 (1997), no. 4, 585–592.

Duzaar, Frank; Steffen, Klaus. Existence of hypersurfaces with prescribed mean curvature in Riemannian manifolds. Indiana Univ. Math. J. 45 (1996), no. 4, 1045–1093.

Duzaar, Frank. Hypersurfaces with constant mean curvature and prescribed area. Manuscripta Math. 91 (1996), no. 3, 303–315.

Duzaar, Frank; Grotowski, Joseph F.  A mixed boundary value problem for energy minimizing harmonic maps. Math. Z. 221 (1996), no. 1, 153–167.

Duzaar, Frank; Fuchs, Martin. Existence of area minimizing tangent cones of integral currents with prescribed mean curvature. Acta Math. Sci. (English Ed.) 15 (1995), no. 1, 95–102.

Duzaar, Frank; Steffen, Klaus. Comparison principles for hypersurfaces of prescribed mean curvature. J. Reine Angew. Math. 457 (1994), 71–83.

Duzaar, Frank. Existence and regularity of hypersurfaces with prescribed mean curvature and a free boundary. J. Reine Angew. Math. 457 (1994), 23–43.

Duzaar, Frank; Grotowski, Joseph F. Energy minimizing harmonic maps with an obstacle at the free boundary. Manuscripta Math. 83 (1994), no. 3-4, 291–314.

Duzaar, Frank; Steffen, Klaus. Boundary regularity for minimizing currents with prescribed mean curvature. Calc. Var. Partial Differential Equations 1 (1993), no. 4, 355–406.

Duzaar, Frank; Steffen, Klaus. λ  minimizing currents. Manuscripta Math. 80 (1993), no. 4, 403–447.

Duzaar, Frank. On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions. Ann. Inst. H. Poincaré C Anal. Non Linéaire 10 (1993), no. 2, 191–214.

Duzaar, Frank; Fuchs, Martin. A general existence theorem for integral currents with prescribed mean curvature form. Boll. Un. Mat. Ital. B (7) 6 (1992), no. 4, 901–912.

Duzaar, Frank; Steffen, Klaus. Area minimizing hypersurfaces with prescribed volume and boundary. Math. Z. 209 (1992), no. 4, 581–618.

Duzaar, Frank; Fuchs, Martin. Einige Bemerkungen über die Existenz orientierter Mannigfaltigkeiten mit vorgeschriebener mittlerer Krümmungsform (Some remarks on the existence of oriented manifolds with prescribed mean curvature form). Z. Anal. Anwendungen 10 (1991), no. 4, 525–534.

Duzaar, Frank; Fuchs, Martin. On integral currents with constant mean curvature. Rend. Sem. Mat. Univ. Padova 85 (1991), 79–103.

 Duzaar, Frank; Fuchs, Martin. Existence and regularity of functions which minimize certain energies in homotopy classes of mappings. Asymptotic Anal. 5 (1991), no. 2, 129–144.

Duzaar, Frank; Fuchs, Martin. Einige Bemerkungen über die Regularität von stationären Punkten gewisser geometrischer Variationsintegrale  (Some comments on the regularity of stationary points of certain geometric variational integrals). Math. Nachr. 152 (1991), 39–47.

Duzaar, Frank. Regularity of  p -harmonic maps into a closed hemisphere. Boll. Un. Mat. Ital. B (7) 5 (1991), no. 1, 157–170.

 Duzaar, Frank; Fuchs, Martin. On removable singularities of  p -harmonic maps. Ann. Inst. H. Poincaré C Anal. Non Linéaire 7 (1990), no. 5, 385–405.

Duzaar, Frank; Fuchs, Martin. Existenz und Regularität von Hyperflächen mit vorgeschriebener mittlerer Krümmung (Existence and regularity of hypersurfaces with prescribed mean curvature). Analysis 10 (1990), no. 2-3, 193–230.

Duzaar, Frank; Fuchs, Martin. On the existence of integral currents with prescribed mean curvature vector. Manuscripta Math. 67 (1990), no. 1, 41–67.

Duzaar, Frank; Steffen, Klaus. A partial regularity theorem for harmonic maps at a free boundary. Asymptotic Anal. 2 (1989), no. 4, 299–343.

 Duzaar, Frank; Steffen, Klaus. An optimal estimate for the singular set of a harmonic map in the free boundary. J. Reine Angew. Math. 401 (1989), 157–187.

Duzaar, Frank. Variational inequalities and harmonic mappings. J. Reine Angew. Math. 374 (1987), 39–60.

Duzaar, Frank; Fuchs, Martin. Corrections to the paper: ``Variational problems with nonconvex obstacles and an integral-constraint for vector-valued functions'' [Math Z. 191 (1986), no. 4, 585–591; MR0832816]. Math. Z. 193 (1986), no. 4, 651.

 Duzaar, Frank; Fuchs, Martin. Optimal regularity theorems for variational problems with obstacles. Manuscripta Math. 56 (1986), no. 2, 209–234.

 Duzaar, Frank; Fuchs, Martin. Variational problems with nonconvex obstacles and an integral-constraint for vector-valued functions. Math. Z. 191 (1986), no. 4, 585–591.

 Bögelein, Verena; Duzaar, Frank; Liao, Naian; Giovanni-Molica; Servadei, Raffaella. Higher regularity theory for (s,p)-harmonic functions. Rendiconti Lincei 35 (2), 311-321.

Bögelein, Verena; Duzaar, Frank; Scheven, Christoph. Evolutionary problems in non-cylindrical domains. Springer INdAM Ser. 46. Springer, Cham, 2021, 43–60.

Agricola, Ilka; Bögelein, Verena; Duzaar, Frank.  In memoriam Thomas Friedrich (1949–2018). Ann. Global Anal. Geom. 56 (2019), no. 4, 613–630.

Duzaar, Frank; Mingione, Giuseppe. Partial differential equations - gradient estimates in non-linear potential theory. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 20 (2009), no. 2, 179–190.

Duzaar, Frank. Optimal regularity for second order parabolic systems via  A-caloric approximation. Riv. Mat. Univ. Parma (7) 4* (2005), 91–113.

Duzaar, Frank; Grotowski, Joseph F.; Steffen, Klaus. Optimal regularity results via  A -harmonic approximation. Springer-Verlag, Berlin, 2003, 265–296. ISBN: 3-540-44051-8

Duzaar, Frank; Steffen, Klaus. The Plateau problem for parametric surfaces with prescribed mean curvature. International Press, Cambridge, MA, 1996, 13–70. ISBN: 1-57146-037-3.

Bögelein, Verena; Duzaar, Frank; Gianazza, Ugo; Liao, Naian; Scheven, Christoph. Hölder Continuity of the Gradient of Solutions to Doubly Non-Linear Parabolic Equations. arXiv:2305.08539

Bögelein, Verena; Duzaar, Frank; Gianazza, Ugo; Liao, Naian; Scheven, Christoph.  Schauder estimates for parabolic p-Laplace systems. arXiv:2507.15722

Bögelein, Verena; Duzaar, Giulia Treu. Parabolic PDEs with Dynamic Data under a Bounded Slope Condition. arXiv:2504.17556