Integral Inequalities of Hardy and Poincare Type

Harold P. Boas, Emil J. Straube
1988 Proceedings of the American Mathematical Society  
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 S is the distance to the boundary, and the positive exponent ß depends on the smoothness of the boundary.
doi:10.2307/2047547 fatcat:vvgn2l76d5h4vo67ciaglyey3y