Harnak inequality for degenerate elliptic equation

GUTIERREZ C. AND TOURNIER F.

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

TAYLOR & FRANCIS INC

Año: 2011 vol. 36 p. 2103 - 2116

0360-5302

Abstract. We obtain Harnack’s inequality for nonnegative solutions to degenerateelliptic equations of the form a(x; y; z)X1;1u+2b(x; y; z)X1;2u+c(x; y; z)X2;2u = 0,where Xi; j are defined with the Heisenberg vector fields and the matrix coecientis uniformly elliptic, and satisfying the additional condition that the ratio betweenthe maximum and minimum eigenvalues is bounded above by a constant biggerthan one that is determined in advance. In the paper we prove critical densityand double ball estimates, once this is established, Harnack follows directly from