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<p>We establish trace and extension theorems for evolutionary equations with the Caputo fractional derivatives in (weighted) <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11118_2025_10205_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> spaces. To achieve this, we identify weighted Sobolev and Besov spaces with mixed norms that accommodate solution spaces and their initial values well-suited for equations involving time-fractional derivatives. Our analysis encompasses both time-fractional sub-diffusion and super-diffusion equations.</p>

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Sobolev Spaces and Trace Theorems for Time-fractional Evolution Equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月12日

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  • Doyoon Kim,
  • Kwan Woo

摘要

We establish trace and extension theorems for evolutionary equations with the Caputo fractional derivatives in (weighted) \(L_p\) L p spaces. To achieve this, we identify weighted Sobolev and Besov spaces with mixed norms that accommodate solution spaces and their initial values well-suited for equations involving time-fractional derivatives. Our analysis encompasses both time-fractional sub-diffusion and super-diffusion equations.