C^{k,\alpha}-regularity of solutions to quasilinear equations structured on H\"ormander's vector fields

TL;DR

This paper establishes H"older regularity of solutions to certain quasilinear equations structured on H"ormander's vector fields, extending known results for linear operators to degenerate nonlinear cases.

Contribution

It proves H"older regularity for solutions of degenerate quasilinear equations based on H"ormander's vector fields, generalizing linear regularity results to nonlinear settings.

Findings

Solutions exhibit H"older continuity under specified conditions.

Regularity results apply to degenerate quasilinear equations.

Extension of linear operator regularity to nonlinear, degenerate cases.

Abstract

For a linear nonvariational operator structured on smooth H\"ormander's vector fields, with H\"older continuous coefficients, we prove a regularity result in the spaces of H\"older functions. We deduce an analogous regularity result for nonvariational degenerate quasilinear equations.