Abstract
We consider positive weak \(C^{1,\alpha }_{loc}\) solutions to
with \(\Omega \) a domain in \(\mathbb {R}^N\), \(p>1\), \(q\ge \max \,\{p/2,1\}\) and \(a(\cdot ,u), f(\cdot ,u)\) are functions satisfying suitable hypotheses. We exploit the Moser iteration technique to prove a Harnack type inequality for the solutions to the linearized equation of (Eq. 0.1). As a consequence we study qualitative properties of solutions to the quasilinear problem (Eq. 0.1) both in bounded domains with a singular set \(\Gamma \) and in \(\mathbb R^N_+\).
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The author is partially supported by Ministerio de Economia y Competitividad under Grants MTM2013-40846-P and MTM2016-80474-P (Spain) and also supported by Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).
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Montoro, L. Harnack inequalities and qualitative properties for some quasilinear elliptic equations. Nonlinear Differ. Equ. Appl. 26, 45 (2019). https://doi.org/10.1007/s00030-019-0591-5
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DOI: https://doi.org/10.1007/s00030-019-0591-5