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arXiv · 2605.25780

Interior a priori estimate for higher order elliptic systems in Orlicz spaces

Amiran Gogatishvili·Pia Salerno·Lubomira Softova
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Abstract

We investigate singular integral operators with variable Calder\'on--Zygmund kernels and their commutators with $VMO$ functions on Orlicz spaces. After revisiting the classical $L^p$ theory, we establish boundedness results in $L^\Phi$ under the standard $\Delta_2$ and $\nabla_2$ conditions on the Young function. The analysis combines decomposition techniques with weak-type estimates to derive the main operator bounds. As an application, these results provide a functional-analytic framework for establishing a priori estimates and proving the interior regularity of solutions to higher-order elliptic equations and systems with discontinuous coefficients.

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Amiran Gogatishvili, Pia Salerno, Lubomira Softova. 2026-05-25. Interior a priori estimate for higher order elliptic systems in Orlicz spaces. https://arxiv.org/abs/2605.25780

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