2021/2023 UNC Greensboro PDE Conference.
Electron. J. Diff. Eqns., Conference 26 (2022), pp. 201-217.

Title: Normal solvability and Fredholm properties for special classes of hypoelliptic operators

Author: Ani Tumanyan (Russian-Armenian Univ., Armenia)
 
Abstract: 
In this work, we establish normal solvability and a priori estimates 
for hypoelliptic operators with special variable coefficients, 
associated with multi-quasi-elliptic symbols, acting in weighted Sobolev 
spaces in R^n. We obtain Fredholm criteria for the special 
classes of regular hypoelliptic operators in various scales of 
multianisotropic spaces. We also provide applications to the smoothness 
of solutions, index invariance on the scale, and spectral properties of 
such operators.

Published May 13, 2025.
Math Subject Classifications: 35H10, 35H30, 47A53.
Key Words: Regular hypoelliptic operator; a priori estimate; Fredholm operator;  multianisotropic weighted space.