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On L^p-solutions to the Laplace equation and zeros of holomorphic functions
dc.contributor.author | Bruna, Joaquim |
dc.contributor.author | Ortega Cerdà, Joaquim |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2007-10-04T15:32:12Z |
dc.date.available | 2007-10-04T15:32:12Z |
dc.date.issued | 1996 |
dc.identifier.uri | http://hdl.handle.net/2117/1224 |
dc.description.abstract | The problem we solve in this paper is to characterize, in a smooth domain $\Omega$ in $\Bbb R^n$ and for $1\le p\le\infty$, those positive Borel measures on $\Omega$ for which there exists a subharmonic function $u\in L^p(\Omega)$ such that $\Delta u=\mu$. The motivation for this question is mainly for $n=2$, in which case it is related with problems about distributions of zeros of holomorphic functions: If $\{a_n\}^{\infty}_{n=1}$ is a sequence in $\Omega\subset\Bbb C$ with no accumulation points in a simply connected domain $\Omega$, and $\mu=2\pi\sum_n\delta_{a_n}$, then all solutions $u$ of $\Delta u=\mu$ are of the form $u=\log |f|$, with $f$ holomorphic vanishing exactly on the poits $a_n$. Thus our results give the characterization of the zero sequences of holomorphic functions with $\log |f|\in L^p(\Omega)$. A related class had been considered by Beller. |
dc.format.extent | 20 pages |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 2.5 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
dc.subject.lcsh | Potential theory (Mathematics) |
dc.subject.lcsh | Partial differential equations |
dc.subject.other | Laplace equation |
dc.subject.other | holomorphic functions |
dc.subject.other | zeros |
dc.title | On L^p-solutions to the Laplace equation and zeros of holomorphic functions |
dc.type | Article |
dc.subject.lemac | Potencial, Teoria del (Matemàtica) |
dc.subject.lemac | Equacions en derivades parcials |
dc.subject.ams | Classificació AMS::31 Potential theory::31A Two-dimensional theory |
dc.subject.ams | Classificació AMS::31 Potential theory::31B Higher-dimensional theory |
dc.subject.ams | Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type |
dc.rights.access | Open Access |
local.personalitzacitacio | true |
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