Existence of Bounded Solutions for Quasilinear Subelliptic Dirichlet Problems

Existence of Bounded Solutions for Quasilinear Subelliptic Dirichlet Problems

Year:    1995

Author:    Chaojiang Xu

Journal of Partial Differential Equations, Vol. 8 (1995), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1995-JPDE-5643

Journal of Partial Differential Equations, Vol. 8 (1995), Iss. 2 : pp. 97–107

Published online:    1995-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

Keywords:    Subelliptic equation

Author Details

Chaojiang Xu