Integral inequalities of Hardy and Poincaré type
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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.
author list (cited authors)
Boas, H. P., & Straube, E. J.