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Mean value theorems for polyharmonic functions: A conjecture by Picone
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Published/Copyright:
February 28, 2014
Abstract
The aim of this paper is to prove a conjecture of Picone concerning a mean value formula for polyharmonic functions. In this formula the mean values are considered on a set of concentric spheres.
Keywords: Polyharmonic functions; mean value theorems
AMS (2010): Primary: 31B30; Secondary: 35B05
Received: 2013-4-17
Accepted: 2014-1-23
Published Online: 2014-2-28
Published in Print: 2014-3-28
©2014 Walter de Gruyter Berlin/Boston
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- Frontmatter
- Embedding theorems corresponding to correct solvability of a linear differential equation of the first order
- On almost asymptotically lacunary statistical equivalent sequences induced probabilistic norms
- A gamma function in two variables
- Mean value theorems for polyharmonic functions: A conjecture by Picone
- The Euler φ-function associated to automorphic L-functions
- Uniqueness and value-sharing of meromorphic functions with finite weight
- Location of the weighted Fermat–Torricelli point on the K-plane (Part II)
- Optimal estimate on Hausdorff dimension of Reifenberg sets
Articles in the same Issue
- Frontmatter
- Embedding theorems corresponding to correct solvability of a linear differential equation of the first order
- On almost asymptotically lacunary statistical equivalent sequences induced probabilistic norms
- A gamma function in two variables
- Mean value theorems for polyharmonic functions: A conjecture by Picone
- The Euler φ-function associated to automorphic L-functions
- Uniqueness and value-sharing of meromorphic functions with finite weight
- Location of the weighted Fermat–Torricelli point on the K-plane (Part II)
- Optimal estimate on Hausdorff dimension of Reifenberg sets
