Summable solutions of some partial differential equations and generalised integral means
S{\l}awomir Michalik
TL;DR
This paper introduces a new way to analyze the summability of solutions to certain multidimensional partial differential equations by using generalized integral means and Pizzetti-type formulas, linking formal solutions to holomorphic properties.
Contribution
It develops a novel characterization of summability for PDE solutions through generalized integral means satisfying Pizzetti-type formulas, extending previous methods.
Findings
Constructed generalized integral means for specific PDE operators
Provided a new criterion for summability based on holomorphic properties
Linked formal power series solutions to integral mean properties
Abstract
We describe partial differential operators for which we can construct generalised integral means satisfying Pizzetti-type formulas. Using these formulas we give a new characterisation of summability of formal power series solutions to some multidimensional partial differential equations in terms of holomorphic properties of generalised integral means of the Cauchy data.
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