The Characterization of the Regularity of the Jacobian Determinant in the framework of Bessel Potential Spaces on Domains

Preprint series: 97-09, Analysis

The paper is published: J. London Math. Soc., 60 (2), 561-580, 1999.

MSC:
46E35 Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems

Abstract: Let $2 \leq m \leq n$. We give necessary and sufficient conditions on the parameters $s_1, s_2, \ldots, s_m, p_1, p_2, \ldots, p_m$ such that the Jacobian determinant extends to a bounded operator from ${\cal H}^{s_1}_{p_1}\times {\cal H}^{s_2}_{p_2} \times \cdots \times {\cal H}^{s_m}_{p_m}$ into ${\cal S}'$.
Here all spaces are defined on ${Bbb R}^n$ or on domains $\Omega\subset {Bbb R}^n$.
In almost all cases the regularity of the Jacobian determinant is calculated exactly.

Keywords: Bessel potential spaces, Jacobian determinant, paraproducts