Campanato-type boundary estimates for Rothe's scheme to parabolic partial differential systems with constant coefficients

Nobuyuki Kato; Norio Kikuchi

doi:10.3934/dcds.2007.19.737

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2007, Volume 19, Issue 4: 737-760. Doi: 10.3934/dcds.2007.19.737

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Campanato-type boundary estimates for Rothe's scheme to parabolic partial differential systems with constant coefficients

Nobuyuki Kato^1, and
Norio Kikuchi^2,

1.
Department of Mathematics, Nippon Institute of Technology, 4-1 Gakuendai, Miyashiro, Minamisaitama, Saitama 345-8501
2.
Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522

Received: January 31, 2006

Revised: June 30, 2007

Published: September 2007

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Abstract

The aim of this paper is to formulate Campanato-type boundary estimates for solutions of the Rothe approximate scheme to parabolic partial differential systems with constant coefficients. The core observation is that such estimates hold independently of the approximate systems.

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Mathematics Subject Classification: Primary: 35K50; Secondary: 93C55.

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Campanato-type boundary estimates for Rothe's scheme to parabolic partial differential systems with constant coefficients

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