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Singular Perturbation on a Subdomain

โœ Scribed by G Aguilar; F Lisbona

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
229 KB
Volume
210
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

We consider a kind of singularly perturbed problem with a small positive parameter affecting the second order derivative only in a part of the domain. We analyse the existence and uniqueness of the solution and the asymptotic behaviour as the small parameter goes to zero.

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where the interface bRl n R = bR2 n R is a "regular" surface with minimal area. This problem has been analyzed, among others, by De Giorgi, Franzone, and Ambrogio in [3] and[4], Can, Gurtin, and Slemrod in [2], Alikakos and Shaing in [l], Modica in [7], Modica and Mortola in [8], Kohn and Sternberg