Unique continuation of positive solutions for doubly degenerate quasilinear elliptic equations

Abstract

We consider quasilinear elliptic equations that are degenerate in two ways. One kind of degeneracy is due to the particular structure of the given vector fields. Another is a consequence of the weights that we impose to the quadratic form of the associated differential operator. Nonetheless we prove that positive solutions satisfy unique continuation property.

Keywords

• Grushin operator
• strong A-infinity weights
• Stummel-Kato classes
• unique continuation