A New Proof of Harnack’s Inequality for Elliptic Partial Differential Equations in Divergence Form
نویسندگان
چکیده
In this paper we give a new proof of Harnack’s inequality for elliptic operator in divergence form. We imitate the proof given by Caffarelli for operators in nondivergence form.
منابع مشابه
Local Bounds, Harnack’s Inequality and Hölder Continuity for Divergence Type Elliptic Equations with Non-standard Growth
We obtain a Harnack type inequality for solutions to elliptic equations in divergence form with non-standard p(x)-type growth. A model equation is the inhomogeneous p(x)-Laplacian. Namely, ∆p(x)u := div ( |∇u|p(x)−2∇u ) = f(x) in Ω, for which we prove Harnack’s inequality when f ∈ Lq0 (Ω) if max{1, N p1 } < q0 ≤ ∞. The constant in Harnack’s inequality depends on u only through ‖|u|p(x)‖p2−p1 L1...
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