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

Alexander M. Meadows

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

Analysis of PDEs 2007-05-23 v1

Authors: Alexander M. Meadows

Abstract

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.

Keywords

semilinear elliptic equations singular solutions of pdes positive solutions of elliptic equations

Cite

@article{arxiv.math/0404422,
  title  = {Stable and singular solutions of the equation $\Delta u = 1/u$},
  author = {Alexander M. Meadows},
  journal= {arXiv preprint arXiv:math/0404422},
  year   = {2007}
}

Comments

20 pages, no figures

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