Hello,

I am interested in what is known about anisotropic Sobolev spaces, by which I mean spaces of functions satisfying

$ \| f \|_p < \infty, \|Df \|_q < \infty, $

where $p \ne q$ (as opposed to the alternate usage signifying that a different Sobolev exponent is imposed on normal versus tangential derivatives). In particular, I am interested in what kinds of trace and embedding results may have been proved about these function spaces. If anyone could suggest a good reference (or even another name by which such function spaces are known), I'd be very grateful. Thanks!