Electron. J. Differential Equations, Vol. 2017 (2017), No. 158, pp. 1-10.

Unique continuation of positive solutions for doubly degenerate quasilinear elliptic equations

Giuseppe Di Fazio, Maria Stella Fanciullo, Pietro Zamboni

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.

Submitted May 17, 2017. Published June 29, 2017.
Math Subject Classifications: 35J70, 35B65.
Key Words: Grushin operator; strong A-infinity weights; Stummel-Kato classes; unique continuation.

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Giuseppe Di Fazio
Dipartimento di Matematica e Informatica
Università di Catania
Viale A. Doria 6, 95125, Catania, Italy
email: giuseppedifazio@unict.it
Maria Stella Fanciullo
Dipartimento di Matematica e Informatica
Università di Catania
Viale A. Doria 6, 95125, Catania, Italy
email: fanciullo@dmi.unict.it
Pietro Zamboni
Dipartimento di Matematica e Informatica
Università di Catania
Viale A. Doria 6, 95125, Catania, Italy
email: zamboni@dmi.unict.it

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