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

Normal solvability and Fredholm properties for special classes of hypoelliptic operators

Ani Tumanyan

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,
DOI: https://doi.org/10.58997/ejde.conf.26.t1

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Ani Tumanyan
Institute of Mathematics
Russian-Armenian University, Armenia
email: ani.tumanyan@rau.am

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