arXiv:math/0404422 Abstract

arXiv:math/0404422 [math.AP]Abstract References Reviews Resources

Stable and singular solutions of the equation $Δu = 1/u$

Published 2004-04-22Version 1

We study properties of the semilinear elliptic equation $\Delta u = 1/u$ on domains in $R^n$, with an eye toward nonnegative singular solutions as limits of positive smooth solutions. We prove the nonexistence of such solutions in low dimensions when we also require them to be stable for the corresponding variational problem. The problem of finding singular solutions is related to the general study of singularities of minimal hypersurfaces in Euclidean space.

Comments: 20 pages, no figures

Categories: math.AP

Subjects: 35J60, 35B34

Keywords: semilinear elliptic equation, study properties, euclidean space, minimal hypersurfaces, general study

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