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<p>We prove the existence of a solution to the obstacle problem for a convection-diffusion parabolic equation whose principal part is of <i>p</i>-Laplacian type, with <i>p</i> in the subcritical range <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="28_2025_1081_Article_IEq1.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left( 1,\frac{2N}{N+2}\right] \)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close="]" open="("> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>2</mn> <mi>N</mi> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mn>2</mn> </mrow> </mfrac> </mfenced> </math></EquationSource> </InlineEquation> and with lower order terms. The operator is not coercive and the obstacle function is time dependent and irregular.</p>

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Noncoercive parabolic obstacle problems in the subcritical case

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月30日

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  • Fernando Farroni,
  • Luigi Greco,
  • Gioconda Moscariello,
  • Gabriella Zecca

摘要

We prove the existence of a solution to the obstacle problem for a convection-diffusion parabolic equation whose principal part is of p-Laplacian type, with p in the subcritical range \(\left( 1,\frac{2N}{N+2}\right] \) 1 , 2 N N + 2 and with lower order terms. The operator is not coercive and the obstacle function is time dependent and irregular.