The Cauchy–Dirichlet problem for a general class of parabolic equations

  • Paolo Baroni

    Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, I-80125 Naples, Italy
  • Casimir Lindfors

    Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, 00076 Aalto, Finland

Abstract

We prove regularity results such as interior Lipschitz regularity and boundary continuity for the Cauchy–Dirichlet problem associated to a class of parabolic equations inspired by the evolutionary p-Laplacian, but extending it at a wide scale. We employ a regularization technique of viscosity-type that we find interesting in itself.

Cite this article

Paolo Baroni, Casimir Lindfors, The Cauchy–Dirichlet problem for a general class of parabolic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 3, pp. 593–624

DOI 10.1016/J.ANIHPC.2016.03.003