Addendum to “Inner transition layers in an elliptic boundary value problem: a necessary condition”: Nonlinear Analysis 44 (4) 487–497 (2001)

✍ Scribed by Arnaldo Simal do Nascimento

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 38 KB
• Volume: 49
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(00)00247-9

✦ Synopsis

In "Inner transition layers in an elliptic boundary value problem: a necessary condition", we addressed the question of ÿnding necessary conditions so that given a ÿnite number of smooth hypersurfaces in an N -dimensional domain each of them would be a transition layer for the problem at issue. Three conditions were found, each of them requiring that the summation of a certain integral over the hypersurfaces vanished. Herein we indicate how to prove that it is actually necessary that each term of the summation vanishes.