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Archive for Rational Mechanics and Analysis

, Volume 216, Issue 2, pp 673–702 | Cite as

Generalized Harnack Inequality for Nonhomogeneous Elliptic Equations

  • Vesa Julin
Article

Abstract

This paper is concerned with nonlinear elliptic equations in nondivergence form
$$F(D^{2}u, Du, x) = 0 $$
where F has a drift term which is not Lipschitz continuous. Under this condition the equations are nonhomogeneous and nonnegative solutions do not satisfy the classical Harnack inequality. This paper presents a new generalization of the Harnack inequality for such equations. As a corollary we obtain the optimal Harnack type of inequality for p(x)-harmonic functions which quantifies the strong minimum principle.

Keywords

Harmonic Function Elliptic Equation Universal Constant Harnack Inequality Nonnegative Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.University of JyvaskylaJyvaskylaFinland

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