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<p>Our objective in this paper is to establish a Harnack inequality for non-negative viscosity supersolutions to equations with lower order terms involving nonlinear gradient terms and whose principal part is a weighted trace operator. We use this to extend the Harnack inequality to viscosity solutions of more general equations with nonlinear absorption and convection terms. Even in the homogeneous case, our results are new and complement the Harnack inequality obtained in the recent paper [<CitationRef CitationID="CR7">7</CitationRef>].</p>

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Local Control of Solutions to Weighted Partial Trace Equations with Nonlinear Gradient Terms

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Ahmed Mohammed,
  • Giovanni Porru

摘要

Our objective in this paper is to establish a Harnack inequality for non-negative viscosity supersolutions to equations with lower order terms involving nonlinear gradient terms and whose principal part is a weighted trace operator. We use this to extend the Harnack inequality to viscosity solutions of more general equations with nonlinear absorption and convection terms. Even in the homogeneous case, our results are new and complement the Harnack inequality obtained in the recent paper [7].