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Domains of dependence for subelliptic wave equations and unique continuation for fractional powers of Hörmander’s operators [PDF]

Nicolas Burq, Claude Zuily
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Nonlinear subelliptic equations

manuscripta mathematica, 2009
The authors define the notion of \(\nu\)-closed Hörmander system of vector fields and study the regularity of solutions to a class of quasilinear elliptic equations connected to a \(\nu\)-closed Hörmander system of vector fields.
Domokos, András, Manfredi, Juan J.
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Exceptional sets for solutions to subelliptic equations

Siberian Mathematical Journal, 1995
This paper deals with removable singularities for bounded solutions of the following class of nonlinear hypoelliptic equations: \[ -\sum^m_{j=1} X^*_jA_j(x,u,X_1u,\dots,X_mu)= f(x,u,X_1u,\dots,X_mu), \] where the \(C^\infty\) vector fields \(X_1,\dots,X_m\) fulfill the well-known Hörmander's conditions for hypoellipticity.
Vodop'yanov, S. K., Markina, I. G.
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Singular subelliptic equations and Sobolev inequalities on Carnot groups

Analysis and Mathematical Physics, 2022
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Garain, Prashanta, Ukhlov, Alexander
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Regularity for quasilinear second‐order subelliptic equations

Communications on Pure and Applied Mathematics, 1992
AbstractIn this paper, we study the regularity of solutions of the quasilinear equation where X = (X1,…,Xm) is a system of real smooth vector fields, Aij, B ϵ C∞(Ω × ℝ Rm+1). Assume that X satisfies the Hörmander condition and (Aij(x, z,ζ)) is positive definite. We prove that if u ϵ S2,α(Ω) (see Section 2) is a solution of the above equation, then u
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A class of subelliptic quasilinear equations

Journal of Global Optimization, 2007
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Schauder estimates for sub-elliptic equations

Journal of Evolution Equations, 2009
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C. E. Gutierrez, LANCONELLI, ERMANNO
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Hölder continuity for quasilinear subelliptic equations in Carnot Carathéodory spaces

Mathematische Nachrichten, 2004
AbstractIn this note we prove the Harnack inequality and the Hölder continuity for weak solutions of quasilinear subelliptic equation of the form where u belongs to Sobolev spaces with respect to a system of locally Lipschitz vector fields. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
DI FAZIO, Giuseppe, ZAMBONI, Pietro
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Liouville-Type Theorem for a Subelliptic Equation with Choquard Nonlinearity and Weight

Mathematical Notes, 2022
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Duong, Anh Tuan, Nguyen, Thi Quynh
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On the Regularity of Nonlinear Subelliptic Equations

2009
We prove C⧜ regularity results for Lipschitz solutions of nondegenerate quasilinear subelliptic equations of p-Laplacian type for a class of Hormander vector fields that include certain nonnilpotent structures.
András Domokos, Juan J. Manfredi
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