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The Principal Eigenvalue¶of a Conformally Invariant Differential Operator,¶with an Application to Semilinear Elliptic PDE

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Abstract:

In this paper we give conditions under which the Paneitz operator, a conformally invariant fourth order differential operator, is positive. We also prove a sharp estimate for a related conformal invariant. These results are combined to study the existence of a semilinear PDE with critical Sobolev growth.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, IN 47405-5701, USA.¶E-mail: gursky@indiana.edu, , , , , , US

    Matthew J. Gursky

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  1. Matthew J. Gursky
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Received: 1 November 1998 / Accepted: 16 April 1999

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Gursky, M. The Principal Eigenvalue¶of a Conformally Invariant Differential Operator,¶with an Application to Semilinear Elliptic PDE. Comm Math Phys 207, 131–143 (1999). https://doi.org/10.1007/s002200050721

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  • DOI: https://doi.org/10.1007/s002200050721

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