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A Fefferman–Phong Type Inequality and Applications to Quasilinear Subelliptic Equations

Potential Analysis, 1999
This paper deals with a nonlocal generalization of a famous C. Fefferman-D. Phong inequality proved in the class \(C^\infty_0(\mathbb{R}^n)\). In the context of the paper under consideration ``nonlocal'' means that the corresponding functional class does not involve compactly supported functions.
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Dirichlet problems for the quasilinear second order subelliptic equations

Acta Mathematica Sinica, 1996
Summary: We study the Dirichlet problem for the quasilinear second-order sub-elliptic equation \[ \sum^m_{i,j= 1} X^*_i(A_{i,j}(x, u)X_j u)+ \sum^m_{j= 1} B_j(x, u) X_j u+ C(x, u)= 0 \quad \text{in }\Omega,\quad u=\varphi\quad \text{on } \partial\Omega, \] where \(X= \{X_1,\dots, X_m\}\) is a system of real smooth vector fields which satisfies ...
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Very weak solutions of nonlinear subelliptic equations

2005
The author proves that if \(u\) is a very weak solution of a nonlinear subelliptic problem with a growth of the nonlinear term of order \(p-1\), which is in \(W_X^{1,r}\), with ...
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SUBRIEMANNIAN GEOMETRY AND SUBELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS