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<p>We study Cauchy problems associated to elliptic operators acting on vector-valued functions and coupled up to the first-order. We prove pointwise estimates for the spatial derivatives of the semigroup associated to these problems in the space of bounded and continuous functions over <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation>. Consequently, we deduce relevant regularity results both in Hölder and Zygmund spaces and in Sobolev and Besov spaces.</p>

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Regularity results for elliptic and parabolic systems of partial differential equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月16日

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  • Luciana Angiuli,
  • Simone Ferrari,
  • Luca Lorenzi

摘要

We study Cauchy problems associated to elliptic operators acting on vector-valued functions and coupled up to the first-order. We prove pointwise estimates for the spatial derivatives of the semigroup associated to these problems in the space of bounded and continuous functions over \(\mathbb {R}^d\) R d . Consequently, we deduce relevant regularity results both in Hölder and Zygmund spaces and in Sobolev and Besov spaces.