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

2026/05/31 by Amiran Gogatishvili, Pia Salerno, Lubomira Softova
Mathematics · #math.AP #msc:30H35 #msc:32A37 #msc:35D35 #msc:35J48 #msc:35J58 #msc:42B20 #msc:42B25 #msc:46E30 #msc:46E35 #msc:47G10

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17 pages

arxiv created 2026/07/31 · arxiv updated 2026/08/03

Abstract

We investigate singular integral operators with variable Calderón--Zygmund kernels and their commutators with VMO functions on Orlicz spaces. After revisiting the classical L^p theory, we establish boundedness results in L^Φ under the standard Δ₂ and ∇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.

Citations

• Density of smooth functions in Musielak-Orlicz-Sobolev spaces W^k,Φ(Ω)
• Higher order elliptic equations in weighted Banach spaces
• Quasilinear elliptic problems with general growth and merely integrable,\n or measure, data
• On the existence of certain singular integrals