Opuscula Mathematica
Opuscula Math. 46, no. 1 (2026), 55-72

A short note on Harnack inequality for k-Hessian equations with nonlinear gradient terms

Ahmed Mohammed
Giovanni Porru
Abstract. In this short note we study a Harnack inequality for \(k\)-Hessian equations that involve nonlinear lower-order terms which depend on the solution and its gradient.
Keywords: \(k\)-Hessian equation, \(k\)-convex solutions, Harnack inequality, Liouville property.
Mathematics Subject Classification: 35J60, 35J70, 35B45, 35B53.
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About the authors ▼
Ahmed Mohammed (corresponding author)
https://orcid.org/0000-0001-5727-3614
Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA
Giovanni Porru
https://orcid.org/0000-0003-1207-5950
Dipartimento di Matematica e Informatica, Università di Cagliari, 09124, Cagliari, Italy
About the article ▼
Communicated by Vicenţiu D. Rădulescu.
Received: 2025-11-15.
Revised: 2025-12-24.
Accepted: 2025-12-26.
Published online: 2026-01-27.
Cite this article as ▼
Ahmed Mohammed, Giovanni Porru, A short note on Harnack inequality for k-Hessian equations with nonlinear gradient terms, Opuscula Math. 46, no. 1 (2026), 55-72, https://doi.org/10.7494/OpMath.202512261.
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