a two-phase free boundary problem for a semilinear elliptic equation

نویسندگان

a. aghajani

چکیده

in this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $dsubset mathbb{r}^{n}$ with smooth boundary‎. ‎we give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of caffarelli and friedman regarding the representation of functions whose laplacians enjoy a certain inequality‎. ‎we show that in dimension $n=2$‎, ‎solutions have optimal growth at non-isolated singular points‎, ‎and the same result holds for $ngeq3$ under an ($n-1$)-dimensional density condition‎. ‎furthermore‎, ‎we prove that the set of points in the singular set that the solution does not have optimal growth is locally countably ($n-2$)-rectifiable‎.

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عنوان ژورنال:
bulletin of the iranian mathematical society

ناشر: iranian mathematical society (ims)

ISSN 1017-060X

دوره 40

شماره 5 2014

میزبانی شده توسط پلتفرم ابری doprax.com

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