Regularity up to the boundary for some degenerate elliptic operators

ABSTRACT

We consider a class of severely degenerate elliptic operators and establish a Harnack inequality up to the boundary. As a consequence, we get smoothness of the weak solutions under very sharp assumptions regarding the lower order terms of the operator.

Keywords:

• Harnack inequality
• Muckenhoupt weights
• degenerate elliptic equations
• Stummel–Kato classes
• Hörmander vector fields

2010 Mathematics Subject Classifications:

• 35B45
• 35B65

Disclosure statement

No potential conflict of interest was reported by the author(s).