Harnack type inequalities and quantization for the uniformly elliptic Liouville equation

Article type: Research Article

Authors: Bartolucci, Daniele | Orsina, Luigi

Affiliations: Department of Mathematics, Università di Roma “La Sapienza”, P. le A. Moro 5, 00185 Roma, Italy. E-mails: {bartoluc, orsina}@mat.uniroma1.it

Abstract: We extend the Harnack type inequality proved in C. R. Acad. Sci. Paris 315(2) (1992), 159–164, to the solutions of -div(A∇u)=Veu in Ω, with no boundary conditions. Here A is a symmetric, uniformly elliptic matrix and Ω⊂R2 is open and bounded. As an application we are able to generalize the quantization results of Ind. Univ. Math. J. 43(4) (1994), 1255–1270, to the uniformly elliptic case.

Keywords: Harnack type inequalities, Liouville equations, uniformly elliptic equations, renormalized solutions

Journal: Asymptotic Analysis, vol. 58, no. 3, pp. 157-169, 2008