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https://doi.org/10.7494/OpMath.202603272

 
Opuscula Mathematica

On a relation between growth estimates and Harnack inequalities for quasilinear elliptic equations with nonlinear lower order terms

Kentaro Hirata

Abstract. We investigate a relation between the Harnack inequalities and the (a priori) growth estimates for positive solutions of quasilinear elliptic equations with nonlinear terms involving the solution and its gradient in an arbitrary domain in \(\mathbb{R}^N\).

Keywords: growth estimate, Harnack inequality, quasilinear elliptic equation.

Mathematics Subject Classification: 35J92, 35B09, 35B45.

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  • Kentaro Hirata
  • Hiroshima University, Department of Mathematics, Graduate School of Advanced Science and Engineering, Higashi-Hiroshima 739-8526, Japan
  • Communicated by Vicenţiu D. Rădulescu.
  • Received: 2025-09-29.
  • Revised: 2026-03-25.
  • Accepted: 2026-03-27.
  • Published online: 2026-05-07.
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