Veröffentlichungen von Christoph Scheven

Veröffentlichungen:

  • (mit K. Moring, S. Schwarzacher und T. Singer) Global higher integrability of weak solutions of porous medium systems. To appear in Commun. Pure Appl. Anal. doi:10.3934/cpaa.2020069

  • (mit V. Bögelein und F. Duzaar) Higher integrability for the singular porous medium system. To appear in J. Reine Angew. Math. (Crelle's Journal).

  • (mit  F. Giannetti und A. Passarelli di Napoli) Higher differentiability for solutions of stationary Stokes systems. To appear in Math. Nachr.

  • (mit K. Moring, S. Schwarzacher und T. Singer) Global higher integrability of weak solutions of porous medium systems. To appear in Commun. Pure Appl. Anal. 

  • (mit Y. Cho) The self-improving property of higher integrability in the obstacle problem for the porous medium equation. NoDEA Nonlin. Diff. Equ. Appl. 16, paper no. 37 (2019). 

  • (mit V. Bögelein, F. Duzaar und L. Schätzler) Existence for evolutionary problems with linear growth by stability methods. J. Differ. Equ. 266, no.11, 7709-7748, 2019. doi:10.1016/j.jde.2018.12.012

  • (mit Y. Cho) Hölder regularity for singular parabolic obstacle problems of
      porous medium type. To appear in Int. Math. Res. Not. (IMRN), doi:10.1093/imrn/rny073

  • (mit V. Bögelein, F. Duzaar, R. Korte) The higher integrability of weak solutions of porous medium systems. Adv. Nonlinear Anal. 8, 1004-1034, 2019. doi:10.1515/anona-2017-0270

  • (mit V. Bögelein, F. Duzaar und T. Singer) Existence of variational solutions in non-cylindrical domains. SIAM J. Math. Anal. 50, no. 3, 3007-3057, 2018. doi:10.1137/17M1156423

  • (mit V. Bögelein, F. Duzaar und P. Marcellini) Doubly nonlinear equations of porous medium type. Arch. Ration. Mech. Anal. 229, 503-545, 2018. doi:10.1007/s00205-018-1221-9

  • (mit T. Schmidt) On the dual formulation of obstacle problems for the total variation and the area functional. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 35, no. 5, 1175-1207 (2018). doi:10.1016/j.anihpc.2017.10.003

  • (mit F. Giannetti und A. Passarelli di Napoli) On higher differentiability of solutions of parabolic systems with discontinuous coefficients and (p,q)-growth. To appear in Proc. Roy. Soc. Edinburgh.

  • (mit V. Bögelein und F. Duzaar) The obstacle problem for parabolic minimizers. J. Evol. Equ. 17(4):1273-1310 (2017), DOI:10.1007/s00028-017-0384-4 

  • (mit V. Bögelein und T. Lukkari) Hölder regularity for degenerate parabolic obstacle problems. Ark. Mat. 55(1), 1-39 (2017), DOI:10.4310/ARKIV.2017.v55.n1.a1 

  • (mit V. Bögelein und F. Duzaar) The total variation flow with time dependent boundary values. Calc. Var. Partial Differ. Equ. 55(4) 55:108 (2016). doi:10.1016/j.anihpc.2017.10.003

  • (mit Thomas Schmidt) BV supersolutions to equations of 1-Laplace and minimal surface type, J. Differ. Equ. 261(3), 1904-1932 (2016), DOI:10.1016/j.jde.2016.04.015

  • (mit F. Giannetti und A. Passarelli di Napoli) Higher differentiability of solutions of parabolic systems with discontinuous coefficients, J. London Math. Soc.(2) 94(1), 1-20 (2016) DOI:10.1112/jlms/jdw019 

  • (mit V. Bögelein und F. Duzaar) The obstacle problem for the total variation flow, Ann. Sci. École Norm. Sup. 49(5), 1139-1184 (2016). doi:10.24033/asens.2306

  • (mit V. Bögelein und F. Duzaar) A sharp quantitative isoperimetric inequality in hyperbolic n-space. Calc. Var. Partial Differ. Equ. 54(4), 3967-4017 (2015). doi:10.1007/s00526-015-0928-9

  • (mit V. Bögelein und T. Lukkari) The obstacle problem for the porous medium equation. Math. Ann. 363 (1), 455-499 (2015) DOI:10.1007/s00208-015-1174-3 

  • (mit A. Gastel) Minimizers of higher order gauge invariant functionals. J. Geom. Anal. 26 (2), 1061-1108 (2016). DOI:10.1007/s12220-015-9584-8 

  • Existence of localizable solutions to nonlinear parabolic problems with irregular obstacles, Manuscripta Math. 146 (1-2) 7-63 (2015). DOI:10.1007/s00229-014-0684-8 

  • (mit V. Bögelein und F. Duzaar) Short-time regularity for the H-surface flow, Int. Math. Res. Not. 12, 3694-3750 (2015). DOI:10.1093/imrn/rnu042

  • (mit F. Duzaar) The evolution of H-surfaces with a Plateau boundary condition, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32(1), 109-157 (2015). DOI:10.1016/j.anihpc.2013.10.003

  • (mit V. Bögelein und F. Duzaar) Global solutions to the heat flow for m-harmonic maps and regularity. Indiana Univ. Math. J. 61(6), 2157-2210 (2012). DOI:10.1512/iumj.2012.61.4819

  • (mit V. Bögelein und F. Duzaar) Weak solutions to the heat flow for surfaces of prescribed mean curvature. Trans. Amer. Math. Soc. 365, 4633--4677 (2013). doi:10.1090/S0002-9947-2013-05885-0

  • Potential estimates in parabolic obstacle problems. Ann. Acad. Sci. Fenn. Math. 37, 415-443 (2012). DOI:10.5186/aasfm.2012.3730

  • (mit V. Bögelein) Higher integrability in parabolic obstacle problems. Forum Math. 24 (5), 931-972 (2012). DOI:10.1515/form.2011.091

  • Elliptic obstacle problems with measure data: Potentials and low order regularity. Publ. Mat. 56 (2), 327-374 (2012). doi:

  • Gradient potential estimates in non-linear elliptic obstacle problems with measure data. J. Funct. Anal. 262 (6), 2777-2832 (2012). DOI:10.1016/j.jfa.2012.01.003

  • (mit V. Bögelein, F. Duzaar  und J. Habermann) Stationary electro-rheological fluids: Low order regularity for systems with discontinuous coefficients. Adv. Calc. Var. 5 (1), 1-57 (2012).

  • (mit V. Bögelein, F. Duzaar und J. Habermann) Partial Hölder continuity for discontinuous elliptic problems with VMO-coefficients. Proc. London Math. Soc. 103 (3), 371-404 (2011).

  • Partial regularity for subquadratic parabolic systems by A-caloric approximation. Rev. Mat. Iberoam. 27 (3), 751-801 (2011).

  • Regularity for subquadratic parabolic systems: Higher integrability and dimension estimates. Proc. Roy. Soc. Edinburgh 140A, 1269-1308 (2010).

  • Nonlinear Calderón-Zygmund theory for parabolic systems with subquadratic growth. J. Evol. Equ. 10 (3), 597-622 (2010). DOI:10.1007/s00028-010-0063-1

  • (mit Thomas Schmidt) Asymptotically regular problems I:  Higher integrability. J. Differ. Equ. 248 (4), 745-791 (2010). DOI:10.1016/j.jde.2009.11.021

  • (mit Thomas Schmidt) Asymptotically regular problems II: Partial Lipschitz continuity and a singular set of positive  measure. Ann. Sc. Norm. Super. Pisa, Cl. Sci. V 8 (3), 469-507 (2009). DOI:10.2422/2036-2145.2009.3.04

  • (mit Andreas Gastel) Regularity of polyharmonic maps in the critical dimension. Commun. Anal. Geom. 17 (2), 185-226 (2009).

  • An optimal partial regularity result for minimizers of an intrinsically defined second-order functional. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (5), 1585-1605  (2009). DOI:10.1016/j.anihpc.2008.07.002

  • Dimension reduction for the singular set of biharmonic maps. Adv. Calc. Var 1, 53-91 (2008). DOI:10.1515/ACV.2008.002

  • Variationally harmonic maps with general boundary conditions: Boundary regularity. Calc. Var. Partial Differ. Equ. 25 (4), 409-429  (2006). DOI:10.1007/s00526-005-0329-6

  • Partial regularity for stationary harmonic maps at a free boundary. Math. Z. 253 (1), 135-157 (2006). DOI:10.1007/s00209-005-0891-9

Sonstige Schriften:

  • Existence and gradient estimates in nonlinear problems with irregular obstacles. Habilitationsschrift, Friedrich-Alexander-Universität Erlangen-Nürnberg, 2011.

  • Zur Regularitätstheorie stationärer harmonischer Abbildungen mit freier Randbedingung. Dissertation, Heinrich-Heine-Universität Düsseldorf, 2004.