Integral inequalities of Hardy and Poincar type Academic Article uri icon

abstract

  • The Poincar inequality | | u | | p C | | u | | p ||u|{|_p} leq C||
    abla u|{|_p}
    in a bounded domain holds, for instance, for compactly supported functions, for functions with mean value zero and for harmonic functions vanishing at a point. We show that it can be improved to | | u | | p C | | u | | p ||u|{|_p} leq C||{delta ^\beta }
    abla u|{|_p}
    , where delta is the distance to the boundary, and the positive exponent \beta depends on the smoothness of the boundary.

published proceedings

  • Proceedings of the American Mathematical Society

altmetric score

  • 3

author list (cited authors)

  • Boas, H. P., & Straube, E. J.

citation count

  • 11

complete list of authors

  • Boas, Harold P||Straube, Emil J

publication date

  • January 1988