Interior Harnack Estimates: The State-of-the-Art for Quasilinear Singular Parabolic Equations

Duezguen F. G., FORNARO S., Vespri V.

MILAN JOURNAL OF MATHEMATICS, vol.83, no.2, pp.371-395, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 83 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1007/s00032-015-0240-3
  • Journal Name: MILAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.371-395
  • Hacettepe University Affiliated: Yes

Abstract

In this paper we give some historical information about elliptic and parabolic Harnack inequalities. Then we state the main results known for Harnack inequalities of solutions to quasilinear degenerate parabolic equations. Lastly we focus our attention on Harnack inequalities of solutions to quasilinear singular parabolic equations where the theory did important steps forward in the last few years but still there are some points to be fully understood.