SOBOLEV INTERPOLATION INEQUALITIES WITH WEIGHTS

We study weighted local Sobolev interpolation inequalities of the form [GRAPHICS] where 1 < p < infinity, h > 1, B is a ball in R(n), and v, w1, and w2 are weight functions. The case p = 2 is of special importance in deriving regularity results for solutions of degenerate parabolic equations. We also study the analogous inequality without the second summand on the right in the case u has compact support in B, and we derive global Landau inequalities parallel-to DELTA-u parallel-to L(w)q less-than-or-equal-to c parallel-to u parallel-to L(v)p1-a parallel-to DELTA-2 u parallel-to L(v)p(a), 0 < a < 1, 1 < p less-than-or-equal-to q < infinity, when u has compact support.