JournalsaihpcVol. 26, No. 5pp. 2001–2024

Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients

  • Fabio Punzo

    Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P.le A. Moro 5, I-00185 Roma, Italy

  • Alberto Tesei

    Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P.le A. Moro 5, I-00185 Roma, Italy
Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients cover
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Abstract

We study well-posedness of the Dirichlet problem for linear degenerate elliptic equations under mild assumptions on the coefficients (in particular, they can be unbounded). We provide sufficient conditions both for uniqueness and nonuniqueness of solutions, which rely on the construction of suitable sub- and supersolutions to certain auxiliary problems.

Cite this article

Fabio Punzo, Alberto Tesei, Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 5, pp. 2001–2024

DOI 10.1016/J.ANIHPC.2009.04.005