We consider positive weak Cloc1,α solutions to -Δpu+a(x,u)|∇u|q=f(x,u)inΩ,with Ω a domain in RN, p> 1 , q≥maxp/2,1 and a(· , u) , f(· , 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 Γ and in R+N.

Harnack inequalities and qualitative properties for some quasilinear elliptic equations

Montoro L.
2019

Abstract

We consider positive weak Cloc1,α solutions to -Δpu+a(x,u)|∇u|q=f(x,u)inΩ,with Ω a domain in RN, p> 1 , q≥maxp/2,1 and a(· , u) , f(· , 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 Γ and in R+N.
Harnack inequalities; qualitative properties; Quasilinear elliptic equations
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/298191
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