Weighted Hardy inequality with higher dimensional singularity on the boundary

@article{Fall2012WeightedHI,
  title={Weighted Hardy inequality with higher dimensional singularity on the boundary},
  author={Mouhamed Moustapha Fall and Fethi Mahmoudi},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2012},
  volume={50},
  pages={779-798}
}
  • M. Fall, F. Mahmoudi
  • Published 31 January 2012
  • Mathematics
  • Calculus of Variations and Partial Differential Equations
Let $$\Omega $$Ω be a smooth bounded domain in $$\mathbb R ^N$$RN with $$N\ge 3$$N≥3 and let $$\Sigma _k$$Σk be a closed smooth submanifold of $$\partial \Omega $$∂Ω of dimension $$1\le k\le N-2$$1≤k≤N-2. In this paper we study the weighted Hardy inequality with weight function singular on $$\Sigma _k$$Σk. In particular we provide necessary and sufficient conditions for existence of minimizers. 
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