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<p>We study the local quasiminimizers of an integral functional exhibiting <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2881_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\( L^{p \&amp; q} \log L\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mrow> <mi>p</mi> <mo>&amp;</mo> <mi>q</mi> </mrow> </msup> <mo>log</mo> <mi>L</mi> </mrow> </math></EquationSource> </InlineEquation> double phase growth. More precisely, some properties of a special double phase type function in the context of Musielak–Orlicz–Sobolev spaces are obtained. We first get Caccioppoli type and Sobolev–Poincaré type inequalities, then we establish that the gradient of a local quasiminimizer has local higher integrability on a bounded domain. We also get boundary higher integrability on a ball for local quasiminimizers. Finally, we explore the existence of weak solutions to certain double phase Dirichlet problems.</p>

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Regularity of K-Quasiminimizers Under \( L^{p \& q} \log L\) Double Phase Growth

  • 期刊论文

  • 发表日期：

    2025年6月23日

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  • Jinxia Cen,
  • Calogero Vetro,
  • Shengda Zeng

摘要

We study the local quasiminimizers of an integral functional exhibiting \( L^{p \& q} \log L\) L p & q log L double phase growth. More precisely, some properties of a special double phase type function in the context of Musielak–Orlicz–Sobolev spaces are obtained. We first get Caccioppoli type and Sobolev–Poincaré type inequalities, then we establish that the gradient of a local quasiminimizer has local higher integrability on a bounded domain. We also get boundary higher integrability on a ball for local quasiminimizers. Finally, we explore the existence of weak solutions to certain double phase Dirichlet problems.