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Weak Solutions of Nonlinear Elliptic Equations with Prescribed Singular Set

✍ Scribed by Yomna Rébaı̈

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
536 KB
Volume
127
Category
Article
ISSN
0022-0396

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✦ Synopsis

Given 0 any open and bounded subset of R n , n 4, with smooth boundary and given 7 any (n&m)-dimensional compact submanifold of 0 without boundary, n>m>2, we prove the existence of weak solutions to the problem &2u=u p in 0

{ u>0 in 0 u=0 on 0, which are singular on 7, when p is a real p>mÂ(m&2), close to this value.

1996 Academic Press, Inc.

&2u=u (n+2)Â(n&2) .

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