On a Priori Estimates and Fredholm Property of Differential Operators in Anisotropic Spaces

Аннотация

The paper is devoted to special a priori estimates and Fredholm property of differential operators acting in anisotropic Sobolev spaces in ℝⁿ. Necessary conditions for a priori estimates in terms of the symbol of an operator are obtained. Under appropriate conditions imposed on the coefficients, a priori estimates are obtained in the corresponding weighted spaces.