Pointwise estimates for the polyharmonic Green function in general domains
Svitlana Mayboroda, Vladimir Maz'ya
TL;DR
This paper derives precise pointwise bounds for the polyharmonic Green function and its derivatives in any bounded domain, advancing understanding of higher-order elliptic operators in complex geometries.
Contribution
It provides the first sharp pointwise estimates for the polyharmonic Green function in general domains, extending previous results limited to special cases.
Findings
Sharp pointwise estimates established for the Green function
Results applicable to arbitrary bounded domains
Enhanced understanding of polyharmonic operators
Abstract
In the present paper we establish sharp pointwise estimates on the polyharmonic Green function and its derivatives in an arbitrary bounded open set.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering