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Please use this identifier to cite or link to this item: http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/11409
Title: Erratum to: Singular Adams inequality for biharmonic operator on Heisenberg Group and its applications
Authors: Dwivedi, Gaurav
Keywords: Mathematics
Heisenberg Group
Biharmonic Operators
Issue Date: 2017
Publisher: Springer
Abstract: We have established Adams-type inequality for biharmonic operator on Heisenberg group and proved the existence of solution to a biharmonic equation involving a singular potential and a nonlinearity satisfying critical and subcritical exponential growth condition. We observed that there is a technical mistake in the homogeneous dimension of the Heisenberg group that is under consideration. For our results to be meaningful, we need to work with bounded domains in H1 instead of bounded domains in H4. The reason of this change is as follows: Let Ω ⊆ Hn be a bounded domain and Q = 2n + 2 be homogeneous dimension of Hn. When Q > 4 (n > 1), we know that D2,2 0 (Ω) → Lq(Ω), 1 ≤ q ≤ 2Q Q−4 . In the critical case, Q = 4(n = 1), D2,2 0 (Ω) → L∞(Ω). Then it is natural to ask, what is the best possible space for this embedding? To answer this question, we need an Adams-type inequality with Q = 4. Thus, we need to work with H1 instead of H4 in [1]. For the sake of clarity, we restate the main results of [1]. However, all the proofs remain unchanged.
URI: https://scholar.google.co.in/citations?view_op=view_citation&hl=en&user=5JlnV8cAAAAJ&citation_for_view=5JlnV8cAAAAJ:IjCSPb-OGe4C
http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/11409
Appears in Collections:Department of Mathematics

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