Regularity for certain nonlinear parabolic systems

Hyeong Ohk Bae, Hi Jun Choe

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

By means of an inequality of Poincaré type, a weak Harnack inequality for the gradient of a solution and an integral inequality of Campanato type, it is shown that a solution to certain degenerate parabolic system is locally Hölder continuous. The system is a generalization of p-Laplacian system. Using a difference quotient method and Moser type iteration it is then proved that the gradient of a solution is locally bounded. Finally using the iteration and scaling it is shown that the gradient of the solution satisfies a Campanato type integral inequality and is locally Hölder continuous.

Original languageEnglish
Pages (from-to)611-645
Number of pages35
JournalCommunications in Partial Differential Equations
Volume29
Issue number5-6
DOIs
Publication statusPublished - 2004

Bibliographical note

Funding Information:
The authors thank the referees. The first author was supported by Korea Research Foundation Grant (KRF-2001-015-DP0020).

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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