Schauder Type Estimates for a Class of Hypoelliptic Operators

TL;DR

This paper extends Schauder estimates to a broad class of higher-order hypoelliptic operators, including certain parabolic equations, providing new regularity results for these complex differential operators.

Contribution

It generalizes Schauder estimates to higher-order hypoelliptic operators and systems, broadening the scope of regularity theory in partial differential equations.

Findings

Schauder estimates are established for higher-order hypoelliptic operators.

Results apply to parabolic equations like ∂_t^2 - ∂_x^3.

The approach extends to systems of such operators.

Abstract

The present paper aims to generalize the Schauder estimate for a class of higher-order hypo-elliptic operators. The results in the present paper apply to parabolic equations of higher order and, for example, operators like $\partial_t^2-\partial_x^3$. Generalization to systems is also directly obtained.