Critical Hardy–Sobolev Inequalities
نویسنده
چکیده
Abstract We consider Hardy inequalities in IRn, n ≥ 3, with best constant that involve either distance to the boundary or distance to a surface of co-dimension k < n, and we show that they can still be improved by adding a multiple of a whole range of critical norms that at the extreme case become precisely the critical Sobolev norm. Résumé Nous étudions des inegalités de Hardy dans IRn, n ≥ 3, avec meilleure constante, liée soit à la distance au bord, soit à la distance à une surface de codimension k < n. Nous obtenons des versions améillorées en ajoutant un certain nombre des normes critiques qui, au cas extrème, sont précisement les normes de Sobolev critiques. AMS Subject Classification: 35J65, 46E35 (26D10, 58J05)
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