WIAS Preprint No. 1950, (2014)

Hölder estimates for second-order operators with mixed boundary conditions


  • ter Elst, A. F. M.
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 35J25 35B65 35D30 35A23


  • Mixed boundary problem, Hölder continuity, kernel estimates




In this paper we investigate linear elliptic, second-order boundary value problems with mixed boundary conditions. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain -- including a very weak compatibility condition between the Dirichlet boundary part and its complement -- we prove first Hölder continuity of the solution. Secondly, Gaussian Hölder estimates for the corresponding heat kernel are derived. The essential instruments are De Giorgi and Morrey-Campanato estimates.

Appeared in

  • Adv. Differential Equations, 20 (2015) pp. 299--360.

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