JournalsaihpcVol. 34, No. 3pp. 593–624

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

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