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<p>This paper presents an existence result and maximal regularity estimates for distributional solutions to degenerate/singular elliptic systems of <i>p</i>-Laplacian type with absorption and (prescribed) locally integrable forcing posed in (possibly unbounded) Lipschitz domains. In particular, the forcing terms may not belong to the dual space of an energy space, e.g., <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(W^{1,p}_{\textrm{loc}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>W</mi> <mtext>loc</mtext> <mrow> <mn>1</mn> <mo>,</mo> <mi>p</mi> </mrow> </msubsup> </math></EquationSource> </InlineEquation>, which is necessary for the existence of weak (or energy) solutions of class <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(W^{1,p}_{\textrm{loc}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>W</mi> <mtext>loc</mtext> <mrow> <mn>1</mn> <mo>,</mo> <mi>p</mi> </mrow> </msubsup> </math></EquationSource> </InlineEquation>. The method of a proof relies on both local energy estimates and a relative truncation technique developed by Bulíček and Schwarzacher (Calc Var Partial Differ Equ 55(3):Art. 52, 14, 2016), where the bounded domain case is studied for (globally) integrable forcing.</p>

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Existence of distributional solutions to degenerate elliptic systems for locally integrable forcing

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  • 发表日期：

    2025年6月12日

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  • Goro Akagi,
  • Hiroki Miyakawa

摘要

This paper presents an existence result and maximal regularity estimates for distributional solutions to degenerate/singular elliptic systems of p-Laplacian type with absorption and (prescribed) locally integrable forcing posed in (possibly unbounded) Lipschitz domains. In particular, the forcing terms may not belong to the dual space of an energy space, e.g., \(W^{1,p}_{\textrm{loc}}\) W loc 1 , p , which is necessary for the existence of weak (or energy) solutions of class \(W^{1,p}_{\textrm{loc}}\) W loc 1 , p . The method of a proof relies on both local energy estimates and a relative truncation technique developed by Bulíček and Schwarzacher (Calc Var Partial Differ Equ 55(3):Art. 52, 14, 2016), where the bounded domain case is studied for (globally) integrable forcing.