Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups , n > 1

By Luca Capogna, Giovanna Citti, Maria Manfredini. 2010

47 citations recorded by the source corpus.

Abstract We prove that Lipschitz intrinsic graphs in the Heisenberg groups , with n > 1, which are vanishing viscosity solutions of the minimal surface equation, are smooth and satisfy the PDE in a strong sense.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cc4956ed517e7138d61a60039001a39f463cfbdd

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In Applied Mathematics

1. Giovanna Citti
2. Maria Manfredini
3. Luca Capogna
4. F. Bigolin
5. Francesco Serra Cassano
6. Raul Paolo Serapioni
7. Valentino Magnani
8. Manuel Ritor'e

In Mathematical Physics

1. Francesco Serra Cassano
2. Giovanna Citti
3. Maria Manfredini
4. Luca Capogna

Citations in the corpus

• Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs (2009, background): “The latter has been in the framework of minimal surfaces in Hn (see [24],[10], [3],[11], [6] and [ 7 ]).”
• Regularity of non-characteristic minimal graphs in the Heisenberg group $H^1$ (2008, methodology): “At this point we introduce an appropriate freezing of the vector fields by defining (3.9) X1,x0 = ∂x1 + (P 1 x0u(x) + s 2)∂x2 , X2,x0 = ε∂x2 and X3,x0 = ∂s. Observe that {X1,x0, X3,x0} is a distribution of smooth vector fields satisfying Hörmander’s finite rank hypothesis with step three.”