Complex powers of second order non-homogeneous elliptic differential operators with degenerating symbols in the spaces \(L_p(\mathbb{R}^n)\)
The authors study complex powers of second-order elliptic differential operators where the principal part has constant real coefficients whereas the first-order terms might have complex coefficients. All considerations are on \(\mathbb{R}^n\). They prove that the negative powers are realized as potential type operators and the positive powers as inverses of approximate operators. The domains of positive powers are determined.
fractional powers of differential operators
scientific article; zbMATH DE number 1744137