Continuous sobolev functions with singularity on arbitrary real-analytic sets

HIGHLIGHTS

• What: The authors investigate a Sobolev property for the reciprocals of logarithms of the modulus of real-analytic functions near their zero sets. The L 1 integrability and the L p -nonintegrability for p > 1 that the authors seek are thus consequences of certain quantitative properties of the level sets of f, which can be conveniently established by utilizing the powerful Hironaka`s resolution of singularities theorem and the Łojasiewicz gradient inequality. The authors show that g ∈ L 1loc (U ).
• Who: Yifei Pan and Yuan Zhang from the (UNIVERSITY) have published the article: Continuous Sobolev . . .
  

   

  

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