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An elliptic system involving a singular diffusion matrix

✍ Scribed by C. García Vázquez; F. Ortegón Gallego

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
609 KB
Volume
229
Category
Article
ISSN
0377-0427

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✦ Synopsis

Let Ω ⊂ R N (N > 1) be a bounded domain. In this work we are interested in finding a renormalized solution to the following elliptic system

where the diffusion matrix A 2 blows up for a finite value of the unknown, say u 2 = s 0 < 0.

We also consider homogeneous Dirichlet boundary conditions for both u 1 and u 2 . In these equations, u 1 is an N-dimensional magnitude, whereas u 2 is scalar; A 2 : Ω ×(s 0 , +∞) → R N is a semilinear coercive operator. The symmetric part of the matrix A 3 is related to the one of A 1 . Nevertheless, the behaviour of these coefficients is assumed to be fairly general.

Finally, f ∈ H -1 (Ω) N , and g : Ω × (s 0 , +∞) → R is a Carathéodory function satisfying the sign condition.

Due to these assumptions, the framework of renormalized solutions for problem (1) is used and an existence result is then established.

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