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On a Free Boundary Problem

✍ Scribed by Abdelkader Boucherif; Sidi Mohammed Bouguima

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
376 KB
Volume
19
Category
Article
ISSN
0170-4214

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✦ Synopsis

This paper considers a discontinuous semilinear elliptic problem:

where H is the Heaviside function, p a real parameter and R the unit ball in R2. We deal with the existence of solutions under suitable conditions on g, h, and p. It is shown that the free boundary, i.e. the set where u = p, is sufficiently smooth.

n,(h) = {x E R; u ( x ) 2 p } and aR,(h) = {x E R; u ( x ) = p } .

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