Let u be a real valued function on an n-dimensional Riemannian manifold M^n. We consider an inequality between the L^q-norm of u minus its mean value over M^n and the L^p-norm of the gradient of u. The best constant in such inequality is exhibited in the following cases: i) M^n is an open ball in IR^n and p=1, 0 < q \leq n/(n−1); ii) M^n is a sphere in IR^{n+1} and either p=1, 0 < q \leq n/(n−1) or p>n, q=∞.

A sharp form of Poincaré inequalities on balls and spheres / A. CIANCHI. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - STAMPA. - 40:(1989), pp. 558-569. [10.1007/BF00944807]

A sharp form of Poincaré inequalities on balls and spheres

CIANCHI, ANDREA
1989

Abstract

Let u be a real valued function on an n-dimensional Riemannian manifold M^n. We consider an inequality between the L^q-norm of u minus its mean value over M^n and the L^p-norm of the gradient of u. The best constant in such inequality is exhibited in the following cases: i) M^n is an open ball in IR^n and p=1, 0 < q \leq n/(n−1); ii) M^n is a sphere in IR^{n+1} and either p=1, 0 < q \leq n/(n−1) or p>n, q=∞.
1989
40
558
569
A. CIANCHI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/204765
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