Dhanya, R and Sarkar, Abhishek (2015) Isolated singularities of polyharmonic operator in even dimension. In: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 61 (1). pp. 55-66.
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We consider the equation Delta(2)u = g(x, u) >= 0 in the sense of distribution in Omega' = Omega\textbackslash {0} where u and -Delta u >= 0. Then it is known that u solves Delta(2)u = g(x, u) + alpha delta(0) - beta Delta delta(0), for some nonnegative constants alpha and beta. In this paper, we study the existence of singular solutions to Delta(2)u = a(x) f (u) + alpha delta(0) - beta Delta delta(0) in a domain Omega subset of R-4, a is a nonnegative measurable function in some Lebesgue space. If Delta(2)u = a(x) f (u) in Omega', then we find the growth of the nonlinearity f that determines alpha and beta to be 0. In case when alpha = beta = 0, we will establish regularity results when f (t) <= Ce-gamma t, for some C, gamma > 0. This paper extends the work of Soranzo (1997) where the author finds the barrier function in higher dimensions (N >= 5) with a specific weight function a(x) = |x|(sigma). Later, we discuss its analogous generalization for the polyharmonic operator.
| Item Type: | Journal Article |
|---|---|
| Publication: | COMPLEX VARIABLES AND ELLIPTIC EQUATIONS |
| Publisher: | TAYLOR & FRANCIS LTD |
| Additional Information: | Copy right for this article belongs to the TAYLOR & FRANCIS LTD, 4 PARK SQUARE, MILTON PARK, ABINGDON OX14 4RN, OXON, ENGLAND |
| Keywords: | elliptic system; polyharmonic operator; existence of solutions; singularity |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 02 Jan 2016 05:31 |
| Last Modified: | 02 Jan 2016 05:31 |
| URI: | http://eprints.iisc.ac.in/id/eprint/52989 |
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