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Solutions with isolated point ruptures for a semilinear elliptic equation in R2 with a non-Lipschitz nonlinearity

✍ Scribed by Zongming Guo; Xingxiao Li

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
344 KB
Volume
17
Category
Article
ISSN
0893-9659

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✦ Synopsis

We study the possible asymptotic behavior of u near an isolated rupture point for the following nonlinear equation with non-Lipschitz nonlinearity:

where B = {x E R 2 : Ix[ < 1}, 0 < q < 1. Under some conditions, the asymptotic behavior of u at zero is characterized. As a result, we obtain the uniqueness of the solutions in R 2 \ {0}.

📜 SIMILAR VOLUMES

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We study the limit behaviour of solutions of the semilinear elliptic equation with a non-Lipschitz nonlinearity on the right-hand side. When |\_+2| 2 we give a complete classification of the types of singularities as x Ä 0 and x Ä which in the rescaled form are essentially non-analytic and, even mo

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## Abstract We consider the DIRICHLET problem for linear elliptic differential equations with smooth real coefficients in a two‐dimensional domain with an angle point. We find an asymptotic representation of the solution near this point, which is stable under small variations of the angle.