Pohozaev-type identities for differential operators driven by homogeneous vector fields

Abstract

We prove Pohozaev-type identities for smooth solutions of Euler-Lagrange equations of second and fourth order that arise from functional depending on homogeneous Hörmander vector fields. We then exploit such integral identities to prove non-existence results for the associated boundary value problems. Date: July 29, 2020. Key words and phrases. sub-elliptic semilinear equations; non-existence results; Pohozaev-type identities; geometric methods for boundary-value problems. The authors are members of INdAM. S. Biagi is partially supported by the INdAM-GNAMPA 2020 project Metodi topologici per problemi al contorno associati a certe classi di equazioni alle derivate parziali. A. Pinamonti and E. Vecchi are partially supported by the INdAM-GNAMPA 2020 project Convergenze variazionali per funzionali e operatori dipendenti da campi vettoriali .