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Volume 8, Issue 2
Existence of Bounded Solutions for Quasilinear Subelliptic Dirichlet Problems

Chaojiang Xu

J. Part. Diff. Eq., 8 (1995), pp. 97-107.

Published online: 1995-08

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  • Abstract
This paper proves the existence of solution for the following quasilinear subelliptic Dirichlet problem: {Σ^m_{j=1}X^∗_ja_j(X, v, Xv)+ a_o(x, v, Xv) + H(x,v, Xv) = 0 v ∈ M^{1,p}_0(Ω) ∩ L^∞(Ω) Here X = {X_1 , …, X_m} is a system of vector fields defined in an open domain M of R^n, n ≥ 2, Ω ⊂ ⊂ M, and X satisfies the so-called Hormander's condition at the order of r > 1 on M. M_{1,p}_0(Ω) is the weighted Sobolev's space associated with the system X . The Hamiltonian H grows at most like |Xv|^p.
  • Keywords

Subelliptic equation weighted Sobolev's space Dirichlet problem

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@Article{JPDE-8-97, author = {Xu , Chaojiang}, title = {Existence of Bounded Solutions for Quasilinear Subelliptic Dirichlet Problems}, journal = {Journal of Partial Differential Equations}, year = {1995}, volume = {8}, number = {2}, pages = {97--107}, abstract = { This paper proves the existence of solution for the following quasilinear subelliptic Dirichlet problem: {Σ^m_{j=1}X^∗_ja_j(X, v, Xv)+ a_o(x, v, Xv) + H(x,v, Xv) = 0 v ∈ M^{1,p}_0(Ω) ∩ L^∞(Ω) Here X = {X_1 , …, X_m} is a system of vector fields defined in an open domain M of R^n, n ≥ 2, Ω ⊂ ⊂ M, and X satisfies the so-called Hormander's condition at the order of r > 1 on M. M_{1,p}_0(Ω) is the weighted Sobolev's space associated with the system X . The Hamiltonian H grows at most like |Xv|^p.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5643.html} }
TY - JOUR T1 - Existence of Bounded Solutions for Quasilinear Subelliptic Dirichlet Problems AU - Xu , Chaojiang JO - Journal of Partial Differential Equations VL - 2 SP - 97 EP - 107 PY - 1995 DA - 1995/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5643.html KW - Subelliptic equation KW - weighted Sobolev's space KW - Dirichlet problem AB - This paper proves the existence of solution for the following quasilinear subelliptic Dirichlet problem: {Σ^m_{j=1}X^∗_ja_j(X, v, Xv)+ a_o(x, v, Xv) + H(x,v, Xv) = 0 v ∈ M^{1,p}_0(Ω) ∩ L^∞(Ω) Here X = {X_1 , …, X_m} is a system of vector fields defined in an open domain M of R^n, n ≥ 2, Ω ⊂ ⊂ M, and X satisfies the so-called Hormander's condition at the order of r > 1 on M. M_{1,p}_0(Ω) is the weighted Sobolev's space associated with the system X . The Hamiltonian H grows at most like |Xv|^p.
Chaojiang Xu . (2019). Existence of Bounded Solutions for Quasilinear Subelliptic Dirichlet Problems. Journal of Partial Differential Equations. 8 (2). 97-107. doi:
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