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<p>We establish partial regularity results for minimizers of a class of functionals depending on differential expressions based on elliptic operators. Specifically, we focus on functionals of Orlicz growth with a natural strong quasiconvexity property. In doing so, we consider both <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\Delta _{2}\cap \nabla _{2}\)</EquationSource> </InlineEquation>-Orlicz growth scenarios and, as a limiting case, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(L \log L\)</EquationSource> </InlineEquation>-growth. Inspired by <span>Conti &amp; Gmeineder</span> (Calc. Var. &amp; PDE 61:215, 2022), the proofs of our main results are accomplished by reduction to the case of full gradient partial regularity results.</p>

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Partial regularity for \(\mathbb {A}\)-quasiconvex functionals with Orlicz growth

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  • 发表日期：

    2026年5月15日

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  • Paul Stephan

摘要

We establish partial regularity results for minimizers of a class of functionals depending on differential expressions based on elliptic operators. Specifically, we focus on functionals of Orlicz growth with a natural strong quasiconvexity property. In doing so, we consider both \(\Delta _{2}\cap \nabla _{2}\) -Orlicz growth scenarios and, as a limiting case, \(L \log L\) -growth. Inspired by Conti & Gmeineder (Calc. Var. & PDE 61:215, 2022), the proofs of our main results are accomplished by reduction to the case of full gradient partial regularity results.