We extend the Harnack type inequality proved in C. R. Acad. Sci. Paris 315(2) (1992), 159-164, to the solutions of -div(A del u) = Ve(u) in Omega, with no boundary conditions. Here A is a symmetric, uniformly elliptic matrix and Omega subset of R-2 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.
Harnack type inequalities and quantization for the uniformly elliptic Liouville equation / Bartolucci, Daniele; Orsina, Luigi. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 58:(2008), pp. 157-169. [10.3233/asy-2008-0879]
Harnack type inequalities and quantization for the uniformly elliptic Liouville equation
BARTOLUCCI, DANIELE;ORSINA, Luigi
2008
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 del u) = Ve(u) in Omega, with no boundary conditions. Here A is a symmetric, uniformly elliptic matrix and Omega subset of R-2 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.File allegati a questo prodotto
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