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<p>Inspired by Frehse’s (Math Z 134 (10):229–230, 1973) work, we show that his elliptic system <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3851_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="113" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta u = F(u, \nabla u)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mi>u</mi> <mo>=</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi mathvariant="normal">∇</mi> <mi>u</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> in the plane has bounded weak solutions <i>u</i> with arbitrarily prescribed singular sets.</p>

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Prescribing singularities of weak solutions of a nonlinear elliptic system in the plane

  • 期刊论文

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  • 发表日期：

    2025年9月16日

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  • Bogdan Petraszczuk

摘要

Inspired by Frehse’s (Math Z 134 (10):229–230, 1973) work, we show that his elliptic system \(\Delta u = F(u, \nabla u)\) Δ u = F ( u , ∇ u ) in the plane has bounded weak solutions u with arbitrarily prescribed singular sets.