Communications in Mathematical Physics

, Volume 224, Issue 2, pp 545–550 | Cite as

Gradient Estimates for the Ground State¶Schrödinger Eigenfunction and Applications

  • Rodrigo Bañuelos
  • Pawel Kröger


Let Ω be a planar convex domain which is symmetric with respect to each coordinate axes. In this paper we give a simple and very short proof, based on the maximum principle, of the sharp lower bound \(\) for the spectral gap of the Dirichlet Laplacian in Ω.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Rodrigo Bañuelos
    • 1
  • Pawel Kröger
    • 2
  1. 1.Mathematics Department, Purdue University, West Lafayette, IN 47907, USA.¶E-mail: banuelos@math.purdue.eduUS
  2. 2.Departamento de Matemática, UTFSM, Valparaíso, Chile. E-mail: pkroeger@mat.utfsm.clCL

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