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<p>We consider systems of elliptic equations, possibly coupled up to the second order, on the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L^p({\mathbb {R}^d};{\mathbb {C}^m})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mi>p</mi> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> <mo>;</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>m</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> scale. Under suitable assumptions, we prove that the minimal realization in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(L^p({\mathbb {R}^d};{\mathbb {C}^m})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mi>p</mi> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> <mo>;</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>m</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> generates a strongly continuous analytic semigroup. We also prove the consistency of the semigroups on the <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> scale and some spectral results.</p>

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Strongly coupled Schrödinger operators in \(L^p({\mathbb {R}^d};{\mathbb {C}^m})\)

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Luciana Angiuli,
  • Luca Lorenzi,
  • Elisabetta M. Mangino

摘要

We consider systems of elliptic equations, possibly coupled up to the second order, on the \(L^p({\mathbb {R}^d};{\mathbb {C}^m})\) L p ( R d ; C m ) scale. Under suitable assumptions, we prove that the minimal realization in \(L^p({\mathbb {R}^d};{\mathbb {C}^m})\) L p ( R d ; C m ) generates a strongly continuous analytic semigroup. We also prove the consistency of the semigroups on the \(L^p\) L p scale and some spectral results.