Regularity for certain nonlinear parabolic systems

Hyeong Ohk Bae, Hi Jun Choe

Research output: Contribution to journalArticle

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 Jan 1

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Nonlinear Parabolic Systems
Regularity
Integral Inequality
Gradient
P-Laplacian Systems
Degenerate Parabolic System
Iteration
Harnack Inequality
Quotient
Scaling

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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Regularity for certain nonlinear parabolic systems. / Bae, Hyeong Ohk; Choe, Hi Jun.

In: Communications in Partial Differential Equations, Vol. 29, No. 5-6, 01.01.2004, p. 611-645.

Research output: Contribution to journalArticle

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AB - 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.

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