Strict starshapedness of solutions to the horizontal p-laplacian in the Heisenberg group

Fogagnolo, Mattia; Pinamonti, Andrea

doi:10.3934/mine.2021046

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2023

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Cited by 2 publications

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“…Roughly speaking, this choice allows to give a sign to the quantity that naturally replaces the term x • ν. We address the interested reader to [16,19,17] for further comments on the notion of star-shaped and some applications.…”

Section: Introductionmentioning

confidence: 99%

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

Biagi¹,

Pinamonti²,

Vecchi³

2020

Preprint

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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 .

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Section: Introductionmentioning

confidence: 99%

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

Biagi¹,

Pinamonti²,

Vecchi³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

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Partial differential equations from theory to applications: Dedicated to Alberto Farina, on the occasion of his 50th birthday

Dipierro

Lombardini

2023

MINE

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Strict starshapedness of solutions to the horizontal p-laplacian in the Heisenberg group

Abstract: We examine the geometry of the level sets of particular horizontally p-harmonic functions in the Heisenberg group. We find sharp, natural geometric conditions ensuring that the level sets of the p-capacitary potential of a bounded annulus are strictly starshaped.

Cited by 2 publications

References 37 publications

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

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

Partial differential equations from theory to applications: Dedicated to Alberto Farina, on the occasion of his 50th birthday

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