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Accepted version

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1997

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/164429

On Lp solutions to the Laplace equation and zeros of holomorphic functions

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Abstract

The problem we solve in this paper is to characterize, in a smooth domain $\Omega$ in $\mathbb{R}^{n}$ and for $1 \leq p \leq \infty,$ those positive Borel measures on $\Omega$ for which there exists a subharmonic function $u \in L^{p}(\Omega)$ such that $\Delta u=\mu$.

Subject

Teoria del potencial (Matemàtica), Equacions en derivades parcials, Funcions holomorfes

Subject (English)

Potential theory (Mathematics), Partial differential equations, Holomorphic functions

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Citation

BRUNA, Joaquim and ORTEGA CERDÀ, Joaquim. On Lp solutions to the Laplace equation and zeros of holomorphic functions. Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. 1997. Vol. 24, num. 571-591. ISSN 0391-173X. [consulted: 10 of June of 2026]. Available at: https://hdl.handle.net/2445/164429

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