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A Survey About the Equation div u=f in Bounded Domains of \(\mathbb{R}^{n}\)


Let \(\varOmega\subset \mathbb {R}^{n}\) be a bounded domain. We review some results about the solution of the equation \(\mathop {\rm div}u=f\), in various functional spaces and under different geometric assumptions on Ω.

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The author would like to thank the referee for helpful remarks.

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Correspondence to Emmanuel Russ.

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Russ, E. A Survey About the Equation div u=f in Bounded Domains of \(\mathbb{R}^{n}\) . Viet J Math 41, 369–381 (2013).

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  • Divergence operator
  • Sobolev spaces
  • Boundary condition
  • Poincaré inequalities

Mathematics Subject Classification (2010)

  • 35F15
  • Secondary: 35C15
  • 35F05
  • 46E35