Geodesic
Harnack inequality for a~class of second-order degenerate elliptic equations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 278 (2012), pp. 7-15

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A second-order degenerate elliptic equation in divergence form with a partially Muckenhoupt weight is studied. In a model case, the domain is divided by a hyperplane into two parts, and in each part the weight is a power function of $|x|$ with the exponent less than the dimension of the space in absolute value. It is well known that solutions of such equations are Hölder continuous, whereas the classical Harnack inequality is missing. In this paper, we formulate and prove the Harnack inequality corresponding to the second-order degenerate elliptic equation under consideration. 
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     author = {Yu. A. Alkhutov and E. A. Khrenova},
     title = {Harnack inequality for a~class of second-order degenerate elliptic equations},
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     url = {http://geodesic.mathdoc.fr/item/TM_2012_278_a0/}
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Yu. A. Alkhutov; E. A. Khrenova. Harnack inequality for a~class of second-order degenerate elliptic equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 278 (2012), pp. 7-15. http://geodesic.mathdoc.fr/item/TM_2012_278_a0/