Integral inequalities of Hardy and Poincaré type Academic Article uri icon

abstract

  • The PoincarÉ inequality ||u||p < C||Vu||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||6"Vu||p, where ᵹ is the distance to the boundary, And the positive exponent δ depends on the smoothness of the boundary. © 1988 American Mathematical Society.

altmetric score

  • 3

author list (cited authors)

  • Boas, H. P., & Straube, E. J.

citation count

  • 10

publication date

  • January 1988