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The embedding theorem in limiting cases and its applications in singular perturbation

The embedding theorem in limiting cases and its applications in singular perturbation In 1980, Brézis[6], using the technique of dividing the total space into two parts, proved the embedding theorem of limiting case which is very important in applications. In 1982, Ding Xiaqi improved the proof given in [6], by using of the technique of dividing the total space into three parts. In this paper, using the technique of dividing the total space into three parts, the author proves uniformly the results obtained by Ding[3,4], and gives an embedding theorem of limiting case including β (Lemma 2.2). And he also gives two kinds of examples, applying the embedding theorems (limiting case and non-limiting case) and the interpolation theorems. These examples are the singular perturbation problems in the sense of Lions[1] (for the definition of singular perturbation, see [1], Introduction). But the singular solutionU e converges uniformly to the limit solution (degenerate)U, ase→0. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

The embedding theorem in limiting cases and its applications in singular perturbation

Zhang, Weitao
Acta Mathematicae Applicatae Sinica , Volume 3 (3) – Jul 13, 2005
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References (8)

Publisher
Springer Journals
Copyright
Copyright © 1987 by Science Press, Beijing, China and Allerton Press, Inc. New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02007664
Publisher site
See Article on Publisher Site

Abstract

In 1980, Brézis[6], using the technique of dividing the total space into two parts, proved the embedding theorem of limiting case which is very important in applications. In 1982, Ding Xiaqi improved the proof given in [6], by using of the technique of dividing the total space into three parts. In this paper, using the technique of dividing the total space into three parts, the author proves uniformly the results obtained by Ding[3,4], and gives an embedding theorem of limiting case including β (Lemma 2.2). And he also gives two kinds of examples, applying the embedding theorems (limiting case and non-limiting case) and the interpolation theorems. These examples are the singular perturbation problems in the sense of Lions[1] (for the definition of singular perturbation, see [1], Introduction). But the singular solutionU e converges uniformly to the limit solution (degenerate)U, ase→0.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jul 13, 2005

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