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2005, Volume 4, Issue 3: 499-522. Doi: 10.3934/cpaa.2005.4.499
This issue Previous Article Existence of periodic solution for a class of systems involving nonlinear wave equations Next Article Non-simultaneous blow-up for a quasilinear parabolic system with reaction at the boundary

Uniformly elliptic Liouville type equations: concentration compactness and a priori estimates

  • 1.

    Department of Mathematics, University of Rome "Tre", Rome

  • 2.

    Department of Mathematics, University of Rome "La Sapienza", Rome

Received:  August 2004
Revised:  March 2005
Published:  September 2005
Abstract Related Papers Cited by
    Abstract
  • We analyze the singular behavior of the Green's function for uniformly elliptic equations on smooth and bounded two dimensional domains. Then, we are able to generalize to the uniformly elliptic case some sharp estimates for Liouville type equations due to Brezis-Merle [7] and, in the same spirit of [3], a "mass" quantization result due to Y.Y. Li [21]. As a consequence, we obtain uniform a priori estimates for solutions of the corresponding Dirichlet problem. Then, we improve the standard existence theorem derived by direct minimization and, in the same spirit of [17] and [37], obtain the existence of Mountain Pass type solutions.
    Mathematics Subject Classification: 35J60, 35J99.

    Citation:
    shu

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