On a class of weighted anisotropic Sobolev inequalities

Details On a class of weighted anisotropic Sobolev inequalities On a class of weighted anisotropic Sobolev inequalities

2007-09-07

arxiv.org/abs/0709.1165v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

In this article, motivated by a work of Caffarelli and Cordoba in phase transitions analysis, we prove new weighted anisotropic Sobolev type inequalities, that is Sobolev type inequalities where different derivatives have different weight functions. The inequalities we are dealing with, are also intimately connected to weighted Sobolev inequalities for Grushin type operators, the weights being not necessarily Muckenhoupt. For example we consider here Sobolev inequalities on finite cylinders, the weights being different powers of the distance function from the top and the bottom of the cylinder. We also prove similar inequalities in the more general case in which the weight is the distance function from an higher codimension part of the boundary.

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